In a medium saucepan, melt the butter over medium-low heat.
Add the onion and jalapeños and cook, stirring occasionally, until softened, about 5 minutes. Add the garlic and Anaheims and cook for 30 seconds longer.
Whisk together the cornstarch, milk and water until well combined, then pour into the pan. Bring to a simmer, stirring constantly, and cook for a couple of minutes until the mixture begins to thicken.
Add the cheese, turn down the heat to low, and cook, stirring, until the cheese has melted. Stir in the cilantro, cumin, cayenne and salt, then taste and adjust the seasonings.
Transfer the queso to a serving bowl or a chafing dish over a flame. Spoon guacamole and pico de gallo into the center of the queso. Serve warm with tortilla chips.