Step 1: Peel the onions. Using a sharp paring knife and starting at the top (opposite the stem end), cut an inverted cone-shaped cavity, about 2 inches across and 1 inch deep. (The core will come out in a cone-shaped plug.) Finely chop the pieces you remove from each onion.
Step 2: Melt 1 tablespoon butter in a skillet. Add the bacon, chopped onion, and chopped jalapenos and cook over medium heat until lightly browned, 4 minutes. Drain the mixture in a strainer over a bowl. Use the bacon fat to brush the outsides of the onions. Place a spoonful of this mixture in the cavity of each onion. Spoon in some barbecue sauce and place a pat of butter (cut from the remaining butter) on top. The recipe can be prepared several hours ahead to this stage.
Step 3: Set up your smoker following the manufacturer’s instructions and preheat to 250 degrees. Add the wood as specified by the manufacturer.
Step 4: Smoke the onions until browned on the outside and tender, 2 to 3 hours. (Foil the onions the last 1-1/2 hours.) Place the grated cheese on top the last 30 minutes. To test for doneness, pinch the sides of the onion—they should be squeezably soft. Transfer the onions to a platter or plates and dig in!