Serves 8
1 medium globe eggplant, peeled, cut into 1/2" pieces
2 pints cherry tomatoes
8 garlic cloves, smashed
1/4 cup extra-virgin olive oil, plus more for skillet
1/2 tsp. crushed red pepper flakes, plus more for sprinkling
Kosher salt
2 large eggs
2 Tbsp. tomato paste
1.5 cups mozzarella, shredded
4 oz. finely grated Parmesan, divided
1 lb. spaghetti
1/2 cup torn basil, plus a few whole leaves
Preheat oven to 425°F. Combine eggplant, tomatoes, garlic, 1/4 cup oil, and 1/2 tsp. red pepper flakes in a large Dutch oven. Season generously with salt and toss to combine. Cook in the oven, stirring once or twice, until eggplant is tender and tomatoes burst, 25–35 minutes. Let vegetables cool while you prepare the pasta (watch out for the hot handle when you take the skillet out of the oven). Reduce oven temperature to 400°F.
Whisk eggs and tomato paste in a medium bowl until smooth, then whisk in about three-quarters of Parmesan.
Cook spaghetti in a pot of boiling salted water, stirring occasionally, until al dente. Immediately drain pasta in a colander and shake to remove excess water; transfer pasta to Dutch oven.
Add egg mixture to pasta and toss vigorously with tongs until pasta is evenly coated. Add 1/2 of the mozzarella and 1/2 cup basil and toss again to combine.
Top with remaining Parmesan, mozzarella, a few whole basil leaves, and an extra sprinkle of red pepper flakes.
Bake pasta until surface is nicely browned, 30–35 minutes. Let cool 10 minutes before cutting into wedges for serving.