Why does melted asiago impart a strong numbing mouthfeel?
Perhaps you are experiencing and allergic reaction.

I got a numb palate and lips from eating sourdough with generous flour on the outside, never had that before. On googling this, it seems it's a form of intolerance. Dry flour baked on a loaf is not the usual way to ingest wheat, and there was a lot of it! Glutens and gliadins in wheat, casein in milk products as well as many other proteins can react with sensitive skin like the mouth.