Heat a grill to high (450° to 550°). Drizzle tomatoes, shrimp, and bread slices (on both sides) with 3 tbsp. oil.
Put cucumber, onion, mint, basil, and capers in a medium bowl and stir to combine.
In a small jar with a tight-fitting lid, combine mustard, salt, pepper, vinegar, and remaining 1/4 cup oil. Cap jar and shake vigorously to emulsify, then pour dressing over cucumber mixture.
Arrange tomatoes and shrimp in a single layer on a grill pan. Grill tomatoes, turning once or twice, until skins begin to char and tomatoes soften, about 4 minutes total. Grill shrimp, turning once, until pink and slightly charred, 3 to 4 minutes total. Let cool slightly.
Grill bread slices directly on cooking grate, turning once, until browned on both sides, about 2 minutes total.
Cut tomatoes in half and add to cucumber mixture along with shrimp; stir to combine. With a vegetable peeler, shave ricotta salata into salad and gently combine. Spoon some dressing onto each slice of bread to moisten, then top each with a quarter of the salad. Serve immediately.