- Prepare your grill with medium flame. Set a large cast iron skillet directly on the grate and allow it to get warm for about 5 minutes.
- Add the olive oil and butter to the cast iron skillet. When the butter is melted, stir in the onion and salt, cover the grill, and cook until the onion is soft, about 5 minutes. Stir in the hatch chiles and, if you’re using them, the jalapeños; cook for another minute or two.
- Add the Miller Lite to the skillet and bring to a simmer, approximately 4 to 5 minutes. Gently add the sausages to the skillet, cover the grill, and cook for about 10 minutes, flipping them halfway through using tongs, until they’re cooked through.
- Transfer the sausages directly to the grill grate and sear each side for 2 to 3 minutes, until they have good grill markings.
- Meanwhile, gradually stir all the cheese into the skillet, stirring after each addition until it’s mostly melted. Season with chili powder. Use good oven mitts to pull the skillet off the grill, or ladle the queso dip into a bowl. Slice the sausages and serve them right away, with toothpicks for dipping.