Preheat oven to 350 degrees F (175 degrees C). Spray an 8-inch square pan with cooking spray.
Heat a large skillet over medium heat. Add ground turkey, onion, and garlic; cook and stir until turkey is browned, 5 to 10 minutes. Stir in diced tomatoes and tomato paste. Add sweet potatoes; cook and stir until slightly softened, about 5 minutes.
Combine eggplant, 1/2 teaspoon tarragon flakes, salt, pepper, chili powder, cumin, oregano, and cardamom in a bowl; toss until eggplant is coated.
Layer coated eggplant on the bottom of the prepared pan; top with turkey mixture.
Bake casserole in the preheated oven until sweet potatoes are lightly browned, about 15 minutes.
Heat a saucepan over high heat. Add olive oil, almond flour, and coconut flour; cook and stir until mixture thickens, about 1 minute. Reduce heat to medium-high. Whisk in almond milk slowly until combined. Cook, continuing to whisk, until sauce is reduced by half, about 10 minutes.
Remove casserole from the oven; cover with sauce.
Bake in the preheated oven until the top of the casserole has browned, 40 to 45 minutes. Top with remaining 1/2 teaspoon tarragon. Slice into 6 pieces with a sharp knife.