"I have no words. If you love big flavors, make this recipe immediately!" —Rach
Bring a large pot of water to a boil for the pasta.
Using a vegetable peeler, peel half of the skin off the eggplant in long strips, leaving a strip of skin between peeled sections. (The eggplant will look striped.) Trim the top and bottom off the eggplant, slice crosswise into about 1/2-inch-thick rounds, then cut into 1/2-inch cubes. Season the eggplant with salt. Let the eggplant drain on a kitchen towel for a few minutes while the sausage cooks.
In a large deep skillet, heat 1 tbsp. oil, one turn of the pan, over medium-high. Add the sausage and cook, stirring occasionally and breaking up the meat, until browned, 5 to 8 minutes. Transfer the sausage to a plate lined with paper towels.
Add the remaining 1 tbsp. oil, another turn of the pan. Pat the eggplant dry. Add the onion and eggplant to the skillet and cook, stirring often, until softened, 3 to 5 minutes. Add the garlic, harissa, cumin, and caraway. Stir until fragrant, a minute or two more. Stir in the vermouth, scraping up the browned bits on the bottom of the pan. Add the tomatoes and sausage. Let the sauce simmer while the pasta cooks.
Cook the pasta about 1 minute less than package directions. Reserve 1/2 cup of the cooking water, then drain the pasta.
Add the pasta, pasta cooking water, cheese, parsley, and mint to the sauce. Toss until the pasta is coated, about 2 minutes. Serve in shallow bowls.