Caramelized Zucchini Phyllo Pie

Name: Caramelized Zucchini Phyllo Pie
Ingredients: 1 (1-pound) package frozen phyllo dough (13x18-inch), thawed in the refrigerator overnight; 1 1/2 pounds zucchini (about 3 medium); 2 medium shallots; 5 tablespoons olive oil, divided; 2 teaspoons kosher salt, divided; 1/2 teaspoon freshly ground black pepper, divided; 1 tablespoon water; 2 large eggs; 1/4 cup tightly-packed coarsely chopped fresh basil leaves, plus whole leaves for garnish; 3 tablespoons coarsely chopped fresh dill; 1 1/2 ounces Parmesan cheese (1 scant cup freshly grated or 1/2 scant cup store-bought); 1 1/2 cups fresh or frozen corn kernels (from about 2 ears fresh); 3 ounces feta cheese (about 1/3 cup crumbled); Hot sauce, for serving (optional)