Preheat oven to 375F.
Place the eggplant in a colander in the sink and season generously with coarse kosher salt; let the eggplant sit like this for 30 minutes.
Add 4 tablespoons olive oil to a large skillet over medium-high heat. Once hot, add the onion and cook until starting to soften, about 5 minutes, stirring occasionally. Add the garlic and cook 1 minute more. Add the tomato, sea salt, smoked paprika, cumin, and black pepper, and cook until the tomatoes are softened, about 5 to 7 minutes. Add the tomato paste and water, and cook until the sauce is thickened, about 5 minutes. Turn off heat.
When the eggplant is done with its salt marinade, rinse each piece off and gently wring out the excess water.
Add the remaining 2 tablespoons olive oil to a large baking sheet. Toss the eggplant in the oil to coat and then arrange the pieces in a single layer cut side down. Bake the eggplant until tender and starting to turn golden, about 25 minutes, flipping once halfway through. To get a little more color on the eggplant, run it briefly under the broiler when it’s done baking (stay with it because it can burn quickly).
To serve, arrange the eggplant on a platter; spoon the sauce on top (re-heat the sauce if you want), and sprinkle on the toasted almonds and fresh mint. Serve warm or at room temperature.