"This sauce gets its pumped-up flavors from a combination of semi-dried tomatoes, sundried tomato paste, sweet vermouth, and spicy Calabrian chile paste, one of my favorite go-to ingredients." —Rach
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 the eggplant lengthwise into 1/4- to 1/2-inch-thick planks, then cut the planks into 2-inch-wide strips. Salt the eggplant, then arrange in a single layer between 2 kitchen towels. Place a heavy skillet on top of the towels to compress and draw the moisture out of the eggplant. Let sit for 15 to 20 minutes.
Bring a large pot of water to a boil for the pasta.
In a deep skillet, heat 2 tbsp. EVOO, two turns of the pan, over medium. Add the garlic and swirl for a minute. Stir in the chile paste, then stir in the vermouth and semi-dried tomatoes. Return to a simmer over medium and let cook until alcohol cooks off, about 2 minutes. Using a wooden spoon, break up the tomatoes, then stir in the passata and basil. Bring the mixture to a bubble over medium-high, then lower the heat to medium-low and let the sauce simmer, stirring occasionally, while you cook the eggplant.
In a large nonstick skillet, heat the remaining 5 tbsp. EVOO, five turns of the pan, over medium to medium-high. Add the eggplant and cook until brown on both sides, 6 to 8 minutes per side.
While the eggplant cooks, salt the boiling water, add the pasta, and cook 1 minute less than the package directions. Reserve 1/2 to 3/4 cup of the pasta cooking water; drain the pasta.
Add the pasta and eggplant to the sauce, adding pasta cooking water as needed to keep the pasta moist and emulsify the sauce. Season. Top the pasta with the cheese and herbs.