Foryoueats: Pasta Primavera

Ingredients

• 1¼ lbs (2 pints) cherry or grape tomatoes, halved
• 4 shallots, thinly sliced
• 5 cloves garlic, peeled and smashed
• ¼ cup extra-virgin olive oil, plus more for serving
• 2 teaspoons salt
• 1½ teaspoons sugar
• 1 medium zucchini, cut into ¼-inch chunks
• 1½ cups fresh corn kernels, from 2 ears corn
• 12 oz fusilli (or similar shape) pasta
• 3 tablespoons unsalted butter
• 1 teaspoon herbes de Provence (see note)
• ⅛ teaspoon crushed red pepper flakes
• ½ cup grated pecorino romano cheese, plus more for serving
• ½ cup tightly packed basil leaves, roughly chopped
• ⅓ cup pine nuts, toasted (see note)