Heat your oven to 475˚F. Roll the dough out on a cornmeal covered tray. Rub with olive oil and layer the squash, shallots, and cheeses. Bake until the crust is crisp and the cheese is bubbly, 15 or so minutes. To make the chili oil, heat a small pan over medium heat. Add the olive oil and warm. Remove from heat and add in the crushed red pepper. Let rest until the flatbread is done.
Drizzle the finished flatbread with the oil, thyme, and flaky salt as desired.
Click here for a printable recipe card.