In a medium saucepan, heat the butter on medium-low. Add the onion and jalapeño and while occasionally stirring cook until softened, about 5 minutes. Add the garlic and cook for 30 more seconds.
Whisk together the cornstarch, milk, and water until well combined then pour into the pot. Bring to a simmer and while stirring cook for a couple of minutes until it begins to thicken, then add the cheese. Turn the heat down to low and while stirring cook until the cheese has melted.
Stir in the green chiles, cilantro, cumin, and cayenne then taste and adjust seasonings, adding salt if needed. If the queso seems too thick, you may thin it with more milk or water.
Transfer the queso to a serving bowl, a slow cooker, or a chafing dish over a flame. Top with the black beans, pico de gallo, and avocado slices. Serve warm with tortilla chips.
Notes
To avoid unwrapping multiple cheese slices, you can get American cheese in blocks from the deli counter at your grocery store. I also like to use Kraft's Deli Deluxe, which has a good flavor and also comes in 1-pound packages, unwrapped.