In a medium saucepot on medium-high heat, add the mustard, beer or tea, cane syrup, hot sauce, white vinegar, Worcestershire sauce, garlic, a pinch of salt and plenty of grinds of black pepper. Simmer until slightly thickened, about 30 minutes.
Heat a grill for indirect cooking to 375 degrees F.
Place the wings on a wire rack, then top with a second wire rack and secure with wire on both sides. Sprinkle on both sides with salt, pepper and a dusting of paprika. Place on the grill over the indirect heat, meat-side down. Close the grill and cook for about 15 minutes. Baste with the sauce, then flip the wings and brush with more sauce. Continue to grill until the wings are golden and the sauce is set and sticky, about 15 minutes more. Serve with the bread and pickles.