Add the eggplant to a colander and season with salt. Let sit for 15 to 30 minutes, then pat with paper towels. The eggplant may start to discolor but that’s ok, it may oxidize as it loses excess moisture.
Heat a large heavy-bottomed pot over medium heat. Add the olive oil and heat through, then add the eggplant and stir occasionally, until golden brown all over, about 6 to 8 minutes. Use a slotted spoon to remove from the pan to a plate, reserving as much oil as possible in the pot.
Return the pot to medium heat, add onion and sauté until just tender, about 4 minutes.
Add the zucchini, summer squash, pepper and stir to combine, cooking until vegetables are softened and golden brown, about 6 minutes. Add the garlic and cook until fragrant, about an additional 30 seconds.
Stir in the tomato paste followed by the vegetable stock and simmer until the sauce thickens and resembles a stew, about an additional 20 minutes.
Bring a large pot of water to a boil over medium-high heat. Add the pasta to the boiling water and cook, stirring occasionally, until al dente, about 10 minutes. Set aside 1 cup (237g) of the pasta water then drain and return the pasta to the pot.
Add the eggplant to the sauce and stir to combine with ½ cup (118g) of the pasta cooking water and ½ cup (118g) of the Parmesan.
Spoon sauce over pasta and stir to combine. Divide pasta among serving bowls and top with additional Parmesan cheese. Serve warm.
Notes
For the best flavor and texture, salt and drain the eggplant before cooking. This step removes excess moisture and prevents the eggplant from becoming soggy or bitter.