How to Make It
Mix cheese, cornstarch, chili powder, and cumin in a large bowl until cheese is coated.
Rub the inside of a saucepan with cut sides of garlic; discard garlic. Add tequila and bring to a simmer over medium. Immediately add cheese mixture a handful at a time, stirring constantly and waiting until cheese has melted and queso is smooth before adding the next handful, about 4 minutes. Stir in chiles, salt, and several grinds of pepper.
Transfer queso to a serving bowl and top with cilantro. Serve immediately with warm tortillas. (To reheat queso, microwave in a microwavable bowl on high until melted, about 1 minute, stirring halfway through.)