It's connected to the bathroom vent and vented that way

I did mine in two of my houses. One I was able to vent out the side which was much easier. The other I had to go through the cabinet above the microwave, through the attic and out the roof. it's quite a bit of work and unless you've done it before, I'd hire out. I'm not sure what they would charge but I'd say it took me about 3-4 hours. It's not much in materials, just tin ductwork, a roof vent, and some aluminum tape. Both of the houses had a soffit above the cabinets so I didn't have to wrap the ductwork between the cabinets and the ceiling.

You'll have to take the microwave down and flip the fan too.


** Caveat **

Even after doing it, it didn't make as huge a difference as I hoped it would. It does help some but those microwave fans are really weak. Anything you cook on the front burners of a stove barely gets pulled in to the fan. If you want anything more than that you're gonna have to replace your microwave with a high-quality hood vent, and they're probably not cheap. Bathroom fans are more effective because it's a small room and you can close the door, which creates somewhat of a vacuum. Most kitchens are open to the main living area of the house which is much larger, so it's more difficult for the fan to do its job unless it's really powerful.

I just want to set your expectations.

Another alternative is a gas grill with a burner and to cook the stuff outside, lol. I eat a ton of fish and that's what I'm gonna start doing, cooking it on the grill.

I’m not a vegetarian, but I love broccoli, Brussels sprouts, asparagus, and other vegetables that are stinky. I don’t like the smell of food in my house after I’ve eaten. I suspect that a survey showed that an over-the-stove microwave oven would be a very popular selling point and would be cheaper than putting in a good range hood that vented through the roof. Range hood venting has to be metal all the way through the roof in case of a fire on the range. Also, a lot of range hoods really don’t suck the heat and smells up very effectively, due to their shape. Some are better than others. Those combined with microwave ovens NEVER work well because they aren’t big enough. You need something that sucks perhaps 300 feet per minute, ideally with the quietest fan you can find, and it has to be rated for stove venting. This is all expensive.

Here’s a cheaper solution I’ve been thinking about. A lot of kitchens here share a wall with the garage. (In some bigger houses, there is a laundry room between the kitchen and the garage.) What if you had a bathroom exhaust fan installed on that wall, perhaps above the door or above the cabinets? There are fans that are ultra quiet but still exhaust 150 cubic feet of air per minute. Just exhaust it into the garage. I think it would be far enough away from the stove so that it wouldn’t count as a stove vent fan or be a fire hazard, but it would vent broccoli smells the same way it vents bathroom smells. You could have it installed with a timer switch so it vents for five minutes to an hour. The smell would then be in your garage, but so what? It might add a little humidity to your garage, but it’s already humid. There’s no insulation to get wet. The only oils it would exhaust is what is already floating through your kitchen.

Here’s one that is inexpensive and goes through the wall and plugs into a wall outlet (it could share with the refrigerator), has an on/off switch in the cord. 576 cubic feet per minute! At 50 decibels, it’s not very quiet—about like your dryer, but no noisier than most range hoods. I once installed a range hood with a fan that vented through the wall and outside, but that was in Pennsylvania. I’m not sure that’s allowed here, or wise, given our rain and winds.

Best way to get unwanted guest to leave early.
Brussels Sprouts with meal, and a couple of pints of Guinness to wash them down.
Lethal combination, and never fail!

It would need to have a certified fire damper to comply with the building code. You cannot have any air openings between the garage and the living space.

vent into the attic and then duct it to the soffit out to the eaves...outdoors

Either sell the house and buy one with hood vented or set your wife up a cooking area on the back lanani.

Actually, cruciferous vegetables (cauliflower, cabbage, kale, bok choy, broccoli, Brussels sprouts, etc) are more nutritious cooked than raw.

And she is .... and anything else that stinks. :D. In our previous home in NJ the stove was against an outside wall and the vent went right thru the wall from the stove. About a total of 18". If I had won the lottery I would have redone the kitchen and moved the stove against the outside wall or just moved to a home with a vent. :D :D. Sadly I'll have to live with Lysol.

Huh? What?

. Thanks for the options. Appreciate it. Sadly we don't have a "lanani" only a lanai. Would that work?

That's what i wanted/hoped to do, but not on my own. The attic isn't easy enough access for my 76 yer old body. The microwave exhaust is totally useless. There are some excellent range hoods out there. Our daughter (also a vegetarian) installed one in her home in VA and you'd never know she cooked a piece of broccoli or a fish even if you were staning next to her stove. If you get too close it will suck you out through the roof. :D

The bottom line is that your plan is doable, but it won't be cheap, and you may need more than one contractor.

Some folks (me)are opposed to microwave cooking.

Cannot vent into an attic, has to vent outside.