Melt the butter in a saucepan over medium heat. Cook onion until translucent, about 4 minutes, then add garlic and cook 30 seconds. Stir in the green chiles and drained tomatoes, cooking 2 more minutes.

Sprinkle cornstarch over the vegetables and stir to coat. Pour in the evaporated milk while whisking, then bring to a gentle simmer until slightly thickened, about 2 minutes.

Reduce heat to low. Add both cheeses a handful at a time, stirring constantly, until completely melted and smooth, 2 to 3 minutes. Stir in cumin and salt to taste.

Spoon the queso into a warm serving bowl, top with cilantro, and serve immediately with tortilla chips.