Light a grill or preheat a grill pan. In a medium bowl, mix the yogurt with the dill pickles and hot peppers and season with salt and black pepper.
In a large bowl, gently knead the turkey with the paprika and 1 1/2 teaspoons of salt. Form the meat into 6 patties, about 3/4 inch thick. Brush the patties with olive oil and season lightly with salt and black pepper. Grill the patties over moderately high heat, turning once or twice, until cooked through, about 12 minutes. Grill the English muffins on both sides until toasted, about 2 minutes.
Spread the pickle sauce on the English muffins. Top with the burgers, lettuce, onion and tomatoes. Close the sandwiches and serve right away.