Prepare the grill to medium-high heat.
To prepare sauce, combine first 3 ingredients; set aside.
To prepare patties, combine shallots and the next 7 ingredients (through turkey breast), mixing well. Divide mixture into 10 equal portions, shaping each into a 1/2-inch-thick patty. Place patties on grill rack coated with cooking spray; grill 4 minutes on each side or until done.
Spread 1 tablespoon sauce on top half of each bun. Layer bottom half of each bun with 1 lettuce leaf, 1 patty, 2 pickles, 1 onion slice, 2 avocado slices, and about 1/3 cup of sprouts. Cover with top halves of buns.