Prepare Dill Sauce: In a small bowl, stir together the yogurt, dill, mustard, olive oil, vinegar, 1/4 teaspoon salt, and 1/8 teaspoon pepper.
Spread a tablespoon of the dill sauce on one side of each of four slices of bread.
Top each slice with lettuce, provolone, tomatoes, a sprinkling of salt and pepper, the cucumber, onion, sprouts, and grated carrot.
Drizzle another tablespoon of dill sauce over each sandwich. Cover with the remaining four slices of bread. Enjoy!