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1
Preheat oven to 375 degrees F (190 degrees C).
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2
Preheat a charcoal grill for medium heat and lightly oil the grate. Poke several holes in the eggplant with a knife.
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3
Grill eggplant, red bell pepper, and green bell pepper until skin starts to blacken and flesh softens, 10 to 15 minutes.
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4
Place eggplant on a baking sheet. Chop red bell pepper and green bell peppers.
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5
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.
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6
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.
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7
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.
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8
Bake in the preheated oven until mozzarella cheese and Parmesan cheese are melted, about 5 minutes.
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9
Toss shrimp with Cajun seasoning in a bowl.
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10
Heat remaining 1 tablespoon olive oil in a skillet. Cook shrimp in the hot oil until opaque, about 3 minutes.
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11
Divide shrimp and tomato slices among flatbreads. Cut into slices or wrap up and serve with remaining eggplant puree on the side.