Heat your broiler. Put the peppers directly under the heat source and broil until the skin blisters and chars, about 5 minutes on each side (keep a close eye on them as cooing time will vary based on your broiler). Let cool. Remove the skin and seeds and chop the peppers into 2-inch pieces.

Cut the tomato into quarters. Remove the skin and seeds.

Add the peppers, tomato, chicken stock, smoked paprika, and cayenne to a medium pot. Simmer 10 minutes, or until the vegetable are very soft and the liquid is mostly absorbed. Transfer to a blender or food processor and blend until smooth (about 30 seconds). Return to pan and stir in heal and half; heat through.

Set a nonstick pan over medium-high heat. Divide the Asiago into four small piles in the hot pan; cook until the cheese begins to crisp, about 1 minute. (The cheese will melt, then begin to bubble. It will be ready to flip with the edges start to brown and the top looks mostly dry) Use a fork to gently flip it over; cook 30 seconds on the other side. Remove from the pan and let cool.

Divide the soup between four bowls. Float asiago crisps in each bowl.