How to Make It
In a large cup, soak the salted capers in plenty of cold water for 15 minutes. Drain the capers and squeeze dry.
Meanwhile, in a large pot of salted boiling water, cook the spaghettini until just al dente. Drain the pasta well, reserving 3/4 cup of the cooking water.
In a large, deep nonstick skillet, heat 1/4 cup of the oil until shimmering. Add the eggplant, season lightly with salt and pepper and cook over high heat, stirring occasionally, until tender, about 6 minutes. Add the sliced garlic and crushed red pepper and cook until the garlic is softened, about 2 minutes.
Meanwhile, in a small skillet, heat the remaining 1/2 cup of oil until shimmering. Add the capers and fry over high heat, shaking the pan slightly, until the capers are golden and puffed, 2 minutes. Using a slotted spoon, transfer the capers to a paper towel–lined plate. Add the whole garlic clove and the diced bread to the oil and fry, stirring, until golden, about 2 minutes. Using a slotted spoon, transfer the croutons to the plate. Discard the garlic clove.
Add the pasta to the eggplant. Add the pecorino and the reserved cooking water and simmer, tossing, just until the water is nearly absorbed, about 2 minutes. Serve the pasta in shallow bowls, sprinkled with the fried capers and croutons. Pass freshly grated pecorino at the table.