Soak the wood chips in water for at least 30 minutes.
Prepare the grill for indirect cooking over medium-high heat (400° to 450°F).
Drain and add the wood chips to the charcoal or to the smoker box of a gas grill, following manufacturer’s instructions, and close the lid. When smoke appears, grill the artichoke hearts over direct heat, with the lid closed, until warmed through, 3 to 5 minutes, turning once. Remove from the grill and roughly chop.
Combine the mayonnaise, cream cheese, mozzarella, chiles, sour cream, garlic, mustard powder, hot sauce, and pepper. Using a wooden spoon, smash the cream cheese against the inside of the bowl into a paste, and then stir the mixture until smooth. Stir in the artichoke hearts.
Related Grill Skills
Lightly grease the inside of an 8-inch cast-iron skillet with butter. Transfer the artichoke mixture to the prepared skillet, and then top evenly with the Parmigiano-Reggiano® cheese. Cook over indirect medium-high heat, with the lid closed, until browned and bubbling on the surface, 20 to 25 minutes. Cool for 10 minutes before serving with grilled baguette slices or crisp flatbread.