What dessert would pair well with a simple avocado ice cream?

Avocado and coconut are great together. I suggest coconut cream pie.

ginger snaps

You could turn the ice cream into cannolis and drizzle with chocolate sauce. Or make a simple crepe to go alongside it drizzled with chocolate or powdered sugar. Or just top it with a nut (pistachio, hazelnut). Or turn it into something more savory and add a lime, chili powder sprinkling of some sort. Or a side of berries or chopped bananas. It will probably do well by itself with a garnish served in a fancy glass (martini, etc.)

Brown butter coconut cookies