Combine cheeses and toss with cornstarch and dried spices. Place cheeses in a heavy-bottomed pot and add milk. Place pot over medium-low heat and stir to melt, 10-15 minutes. Add onions, garlic and chilies, and reduce heat to low. Stir to combine flavors and cook onions, 10 minutes more. Keep warm over low heat, stirring occasionally for 1 hour or serve in slow cooker on low setting.
Serve queso on hot dogs garnished with jalapeño chips or pickled jalapeños; build nachos with spiced ground beef or crumbled Mexican chorizo; serve with jicama, radishes and celery hearts for dipping; use as a topping for crispy Tater Tots hot from the oven or slather the queso on grilled corn.