Combine 1 1/2 teaspoons hoisin, 1 1/2 teaspoons soy sauce, ketchup, mustard, sesame seeds, oil, and 1/4 teaspoon chile paste in a small bowl.
Place tofu on a foil-lined baking sheet coated with cooking spray. Brush tofu with half of hoisin mixture; broil 6 minutes or until browned. Turn tofu over; brush with remaining hoisin mixture. Broil 6 minutes or until browned. Cover; keep warm.
Combine 2 tablespoons hoisin, 1 tablespoon soy sauce, 1/4 teaspoon chile paste, broth, and garlic in a Dutch oven. Bring to a boil; cook for 2 minutes. Add spinach; cook until wilted. Stir in noodles. Spoon 1 1/2 cups noodle mixture into each of 4 large bowls; top each serving with 3 tofu slices.
Note: Look for chile paste and udon noodles in the Asian section of the supermarket or at specialty Asian markets.