Heat the oven to 425°F
Cut the eggplant into 1-inch dice and toss it on a rimmed baking sheet with enough olive oil to coat. Sprinkle with sea salt. Roast in the oven until browned and very tender, about 20 minutes. You will know it is done when it is nice and creamy and you can easily squish it between your fingers.
While the eggplant is roasting, chop your tomatoes, garlic, and herbs and bring a big pot of water to a boil. Add the pasta and cook according to the package instructions.
Heat 4 tablespoons of olive oil in a large skillet over medium heat until it shimmers. Add the garlic and basil or parsley and cook, stirring, until the greens are completely wilted and dark green, about 1-2 minutes. Be sure to stir constantly so the garlic does not stick to the pan and burn.
Add the tomatoes and a pinch of sea salt and cook for about 5 minutes until softened. The sauce should develop as the tomatoes release their juices.
At this point, the eggplant should be done. Add the roasted eggplant to the skillet and turn to low to let the sauce simmer gently.
Drain the pasta, reserving about 1 cup or the pasta water. Toss the pasta with the sauce and the mint. If the mixture seems dry, add some of the pasta cooking water, a little at a time, until the sauce is your desired consistency. Taste and add additional salt, if needed.
Serve warm and sprinkle with grated parmesan.