Anyone have an idea on how to fill this gap -- about a half-inch wide? I was thinking I would try to just compression fit a sliver of sheetrock and then smooth with joint compound and spritz with Homak texture. Wondering if someone might have a better idea.

Spray Foam. Let it fill, cut back with razor knife and texture over it.

Of course! Thank you for sharing your common sense!

^ what he said, foam, but tape/wrap that brick first; the foam will stick to the brick like super glue!

Thank you oldoak!

Of course, tape off what you don't want the spray foam to stick to. Use the blue stuff and just slice it off. After you cut the foam off flush with the wall you can sand it to get it sub surface to the wall so your thin layer of mud will have a place to go.

If you want extra security from cracking, use a razor knife to cut through the sheet rock paper, about 1/2 inch all the way around your hole and inset some fiberglass tape and mud over until it's smooth.

That actually sounds like a better idea.

That’s not a bad spot by my standards. I repaired a spot 20 times larger with joint compound from when my ex’s Labrador tried to chew his way through the wall. Luckily he hit a stud