Who made the hood cover? Were they given the specs for the insert? Why was the hood cover made at 19 inches deep if the insert was 21 inches deep? What are the hood cover makers suggestions on how to make this right?

@vinmarks long story short, the hood was gifted to us which is why there's no way to return/contacting the makers. We'd like to make it work if we can

post picture straight on - can you build out back wall ? vs trim around hood?

Could you tile behind it and leave the gap? You could cover the braces with trim. Just a thought.

Maybe fur out the wall (the depth of the gap) on each side, 6" or so, at the bottom of the hood to the counter (would look like columns on each side of the range/cooktop). Have the dry-wall sheet extend to the blocking behind the cover, following the curve of the hood. Then tile it all, and do a feature over the range, to make it look planned. I'm thinking that any solution is going to be just as expensive, if not more so, than replacing the hood cover.

We don't have space to build out that wall because there's a door opening next to the countertops that's 25" from the wall (almost flush with perimeter cabinets), but we were thinking about using unfinished wood veneer banding + extending the top and bottom trim if we're able to match it?

Thanks-- as mentioned fir out the back wall to build out to be flush w the gap- I think you could just fir out the area from the bottom of the vent hood-- or another suggestion is to see if you can use that foam sealer (comes in a spray can) to fill in the gap (fill gap with a mesh tape)- let dry and use a knife to cut to follow lines, Spackle to accommodate air bubbles in foam and paint -- it will take time and a steady hand -- I had to do this with a stone wall matching up to a dry wall ceiling

New hood time.

Go buy one for every room. https://www.harborfreight.com/10-ft-carabiner-tape-measure-65999.html 

Can the hood insert be cut down at all or recessed in to the wall at all?

This gift of a hood is not really a gift. It's a burden. It will cost you in money and aggravation, and even then, will never be right. Even if you can fix the insert issue, the hood is too shallow to cover the front burners, so it won't exhaust whatever you are cooking on the front burners. Sell it and the insert on Craig's List, and buy a proper metal hood with baffle filters (not mesh) that is 24" deep front to back.

I know I'm late but.... You could add color changing LED lights on the back edge so it glows all around the edge like its floating. Just tell everyone you designed it that way ;-)