Lay a few paper towels over the eggplant and press down to squeeze out additional moisture. Line a sheet pan with parchment and scatter the eggplant cubes on the parchment paper.
While the eggplant roasts, start the sauce and cook the pasta. Heat the remaining 2 Tbsp olive oil over medium heat in a dutch oven or large saute pan.
Stir in the diced tomatoes and cook for about 10 mins. Stir in the white wine and cook until reduced by half. Add the pecorino cheese, 1 cup pasta water, sugar, and seasonings.
Toss all of the ingredients together in the pot very well just before serving. The mozzarella will begin to melt and the basil should still taste fresh and bright.