Melt the butter in a small skillet over medium heat. Add the diced onion and cook for 5-8 minutes until softened and beginning to caramelize. Add the garlic and stir, cooking for an additional 30 seconds until fragrant. Remove from the heat and set aside.
Heat the milk in a medium saucepan over medium heat until small bubbles form on the edges of the saucepan. Reduce the heat to low.
Add the cheese cubes ½ cup at a time and continuously stir into the heated milk with a whisk until they are fully incorporated and melted. Continue this process until all the cheese cubes are melted, making sure to gently and continuously whisk the queso dip until it is smooth and silky.
Remove the saucepan from the heat and gently stir in the cooked onions and garlic, the diced green chiles, salt, and black pepper. Stir in any additional milk as needed if the queso becomes too thick.
Garnish with chopped tomatoes and jalapeños, and serve with your favorite tortilla chips.
Notes
Continuously whisking the queso dip can be tedious, but this is an important step so that the queso doesn’t become grainy and lumpy. Slowly and gently melting the cheese is what gives you a smooth consistency.
If you prefer your queso a little more runny, add more milk. You could also stir in some salsa at the end to thin it out.