Preheat the smoker or grill to 250 degrees F. *If smoking, add 1-2 small wood chunks or a small handful of wood chips.
Add the cubed cheeses, canned green chiles, garlic powder, smoked paprika, and cumin to a half-size deep aluminum steam pan or large cast iron skillet in an even layer. Add about ½-¾ cup of evaporated milk to the pan or skillet, reserving some to adjust the thickness of the dip later.
Place the pan on the smoker or grill. Lay the whole jalapeños on the grill grates as well. Close the grill lid and smoke the queso dip for 15-20 minutes. Then stir the dip. Continue cooking the queso for a total of 1 - 1½ hours, stirring every 15 minutes, until the cheeses are fully melted.
If you want a thinner dip consistency, add the remaining evaporated milk. You can add the milk in ¼ cup intervals, stirring as you go, until you get your desired consistency.
When the queso dip is finished cooking, seed and dice the smoked jalapeños. Stir into the smoked queso dip. For a spicier dip, you may leave the seeds in the peppers.
Optional - Garnish the top of the dip with sliced green onions, additional diced jalapenos, or your favorite Mexican garnishes.
For best results, serve the queso dip in a slow cooker set to warm. Stir the dip occasionally so that it remains smooth and creamy.