Place the ground turkey in a large mixing bowl.
Add the minced garlic, sliced green onions, chopped sun-dried tomatoes, bread crumbs, and lemon zest to the bowl.
Mix the ingredients gently with your hands until just combined, then season lightly with salt and pepper to taste.
Divide the mixture into 4 equal portions and form each into a patty, handling as little as possible; press a slight indentation in the center of each patty.
Soak mesquite (or preferred) wood chips or small chunks in water for a few minutes, then prepare your grill with hot coals or heat your gas grill.
When coals are white hot, place them in the BBQ and add the soaked wood on top, then replace the grill rack and close the lid to allow smoke to build.
Position the patties on the grill, close the lid but leave it slightly cracked so smoke can escape, and avoid direct flames.
Smoke the patties 5–7 minutes per side, flipping once, until cooked through and internal temperature reaches 165°F (74°C).
Remove the burgers from the grill and let them rest briefly before serving.