Grilled Shrimp with Charred Peppers with Queso Blanco

Name: Grilled Shrimp with Charred Peppers with Queso Blanco
Ingredients: 2 lb. poblano peppers (about 5); 1/2 lb. mini sweet peppers; 2 bell peppers (yellow and orange); 2 jalapeños; 2 1/2 tbsp. olive oil, divided; 1 3/4 lb. extra-large shrimp, peeled and deveined; Kosher salt and pepper; 1 lime; 1/2 c. tortilla chips, finely crushed; 1 tbsp. cilantro, finely chopped; 1/2 c. half-and-half; 6 oz. Monterey jack cheese, coarsely grated; 3 slices white American cheese