Preheat your oven to 400°F (200°C).
Toss the sliced eggplant with 3 tablespoons of olive oil, salt, and pepper.
Spread the eggplant slices in a single layer on a baking sheet and roast for about 25-30 minutes, flipping halfway through.
Heat 6 tablespoons of olive oil in a large skillet over medium heat, add the quartered cherry tomatoes, 3 teaspoons of salt, and 1 teaspoon of sugar. Cook until tomatoes soften, about 5-7 minutes.
Pour in 1 cup of water and add the cider vinegar. Bring to a simmer for about 10 minutes.
Stir in 1 tablespoon of Tabasco hot sauce and season with black pepper.
Add the roasted eggplant to the skillet and gently stir to combine.
Remove from heat and fold in the freshly sliced basil and chopped mint.
