Add 3 to 4 large fistfuls of apple wood chips into a bowl and cover with water. Soak for 30 minutes.
Meanwhile, add the lean ground beef into a skillet with onion and garlic. Cover over medium, stirring often and breaking up the meat with a wooden spatula. Cook until no longer pink. Drain and discard any fat in the pan.
Transfer meat mixture to a disposable pan.
Then add in diced tomatoes and green chiles, jalapeño, taco seasoning and mix to combine. Add all of the cheese and again, carefully toss to combine.
Pour in 1 cup half and half.
Preheat outdoor gas grill on high for 15 minutes.
Once hot, clean grates and use tongs to open the smokebox. Use the same tongs to grab the soaked wood chips (2 to 3 tongs full), dripping excess water back into the bowl and add to the smokebox and then close the lid. Ignite the burner under the smoke box.
Close the grill lid, turn off all burners except for the one under the smokebox to maintain a grill temp of 250-300°. You may need to adjust the heat under the smokebox to control the grill temp.
Smoke the queso for 30 minutes. Then cover with heavy duty foil and continue to "grill" at 250-300° for another 30 minutes.
Use oven mitts to move the queso to a rimmed baking sheet. Stir well to combine and add more half and half if needed - you can do this on the grill while the dip is warm or heat the half and half in a sauce pan and add it off the grill.
Serve with tortilla chips.