Skillet Phyllo Pie with Butternut Squash, Kale, and Goat Cheese

olive oil, plus more for brushing

medium red onions, finely chopped

small butternut squash (about 1 pound), peeled, cut into 3/4-inch pieces

chopped thyme

crushed red pepper flakes

bunch Tuscan kale, ribs and stems removed, thinly sliced crosswise

large eggs, beaten to blend

Parmesan, grated

finely grated lemon zest

Kosher salt, freshly ground pepper

frozen phyllo pastry, thawed (half a 1-pound package)

fresh goat cheese or feta, crumbled