Preheat a charcoal grill for medium heat and lightly oil the grate. Poke several holes in the eggplant with a knife.
Grill eggplant, red bell pepper, and green bell pepper until skin starts to blacken and flesh softens, 10 to 15 minutes.
Place eggplant on a baking sheet. Chop red bell pepper and green bell peppers.
Bake eggplant in the preheated oven until soft, about 20 minutes. Cool until easily handled, about 10 minutes. Peel off skin. Mash flesh into a coarse paste.
Combine mashed eggplant, tahini, lemon juice, garlic, and cumin in a blender; puree until smooth. Pour into a bowl. Drizzle 1 tablespoon olive oil on top.
Arrange flatbreads on a baking sheet. Spread 2 tablespoons eggplant puree and 1 teaspoon pesto on top of each flatbread. Top with 1/4 cup red bell pepper, 1/4 cup green bell pepper, 1 cup mozzarella cheese, and 1/4 cup Parmesan cheese.
Bake in the preheated oven until mozzarella cheese and Parmesan cheese are melted, about 5 minutes.
Toss shrimp with Cajun seasoning in a bowl.
Heat remaining 1 tablespoon olive oil in a skillet. Cook shrimp in the hot oil until opaque, about 3 minutes.
Divide shrimp and tomato slices among flatbreads. Cut into slices or wrap up and serve with remaining eggplant puree on the side.