For Smoked Caprese Salad: Thinly slice the smoked mozzarella and arrange on a platter with thinly sliced smoked tomatoes. Strew with torn fresh basil leaves, drizzle with extra virgin olive oil and balsamic vinegar, and season with salt and pepper.
Step 1: Place a small mound of charcoal in the smoker firebox or to one side of a kettle grill and light it. Brush and oil the grate. When the coals glow red, place the cheese in the smoke chamber (or on the side of the kettle grill opposite the embers), as far away as possible from the fire. Toss the hay on the coals and close the smoker or cover the grill. Smoke the cheese until it’s colored with smoke (but not long enough to melt it), 2 to 4 minutes.
Step 2: Slide a spatula under the cheese and transfer it to a plate to cool. Do not grab it when hot, or the deposit of smoke will come off on your fingers. Serve once it has cooled to room temperature, or refrigerate until serving. (For maximum flavor, let the cheese warm to room temperature before serving.) Drizzle with olive oil and/or salt, if desired, and serve.
Other ways to eat it:
Smoked Mozzarella Panini: Place sliced smoked mozzarella and thinly sliced speck (Italian smoked ham), prosciutto, or tomatoes in a square of focaccia (slice it in half through one side) to make a sandwich. Brush the outside with olive oil and toast on the grill (place a grill press on top) or in a sandwich press until crusty and brown and the cheese starts to melt.
Smoked Eggplant Parmigiana: Place slices of smoked mozzarella atop slices of grilled or fried eggplant. Top with tomato sauce and grated Parmigiano-Reggiano cheese. Indirect-grill or bake until browned and bubbling.