Preheat oven to 425 degrees (F). Coat a large baking sheet with olive oil. Arrange eggplant rounds in a single layer. Sprinkle generously with salt and freshly ground black pepper. Roast, without flipping, 25 minutes. Carefully flip each piece: the undersides should be dark and blistered - If they’re not, let them roasted longer. Once flipped, sprinkle them with additional salt and freshly ground black pepper and return the pan to the oven for another 15-18 minutes, or until the undersides match the tops.
For the fresh tomato skillet sauce:
Quarter tomatoes and place them in a large mixing bowl. Sprinkle with salt and sugar, cover tightly with saran wrap, and set aside for 10 minutes.
Heat a large heavy skillet over medium-flame. Add 3 tablespoons of olive oil and warm until it begins to shimmer. Add tomatoes and all of their juices, stir to coat. Cook tomatoes on medium - stirring frequently - for 20 minutes, gently breaking up any large chunks of tomato with the back of a wooden spoon.
At the 20 minute point, add 1/4 cup water, the vinegar, and the hot sauce. Stir to combine and cook for another 10 minutes. Add another 1/4 cup of water, stir, and cover partially. Simmer for 15 minutes. Add more water if sauce appears to thick. Stir in remaining oil, black pepper, basil, and mint. Taste and adjust seasoning as needed.
When ready to serve, ladle about a 1/4 of sauce over top 2 pieces of eggplant, plate, and serve at once!
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