Step 1

Melt butter over medium-high in a large pot. Add onion and garlic; cook, stirring often, until onions are tender, about 5 minutes. Stir in chiles and salt, cooking just until heated through, 1 to 2 minutes. Add half-and-half, and continue stirring until warmed throughout and beginning to steam, about 5 minutes.

Step 2

Toss together cheeses and cornstarch in a small bowl. Reduce heat to medium, and add cheese, 1 handful at a time, whisking after each addition. Once fully melted and smooth, remove from heat. Serve immediately with tortilla chips. Add additional stir-ins, if desired.