Move an oven rack to the second highest rung. Turn the broiler on high. Arrange the tomatoes, Anaheim peppers, tomatillos, serrano peppers, and garlic cloves (in their papery skin) on a large baking sheet in a single layer.
3 Roma tomatoes, 5 Anaheim chili peppers, 4-5 medium tomatillos, 2 serrano peppers, 4 cloves garlic
Roast the vegetables for 6-8 minutes until they start to soften and char. Remove the garlic cloves and set aside. Use tongs to carefully flip the peppers, tomatillos, and tomatoes, then return them to the oven to broil on the other side for another 6-8 minutes until charred on both sides. Remove from the oven to cool.
Remove the stem and seeds from the Serrano and Anaheim peppers. Peel the charred skin off the tomatillos and tomatoes. Remove the papery skin from the garlic cloves.
In a blender, combine the serrano peppers, tomatillos, 1 of the roasted tomatoes, the garlic cloves, and the salt. Blend until smooth and set aside.
1/2 teaspoon kosher salt
Dice the green chiles into 1/2-inch pieces and set aside. Chop the tomatoes and set aside.
In a heavy bottom skillet or dutch oven, melt the butter over medium heat. Add the minced garlic and saute for 30 seconds. Add the diced green chiles and reserved chopped tomatoes, sauteing for another 30 seconds.
1 Tablespoon salted butter, 1 clove garlic
Add the half-and-half, cubed American cheese, and ancho chili powder. Stir frequently over medium heat until completely melted and smooth.
2 cups half-and-half, 1/8 teaspoon ancho chili powder, 1 pound white American cheese
Add the cheddar cheese and reserved salsa verde mixture. Stir until everything is melted, then remove from the heat and enjoy immediately or set aside for 2-3 hours to allow the flavor of the chiles to infuse into the cheese. Rewarm over gentle heat on the stovetop or in a slow cooker.
1 cup freshly grated sharp cheddar cheese
To serve, place a few tablespoons of guacamole in a bowl. Spoon the hot queso over the guacamole, then drizzle with hot sauce and sprinkle with cotija cheese and chopped cilantro. Serve with tortilla chips.
Guacamole, Finely chopped fresh cilantro, Grated cotija cheese, Hot sauce, Tortilla chips