Preheat the oven to 500° with the rack in the middle of the oven. Butter an 8-by-10-inch Detroit-style pizza pan, a brownie pan, a cast-iron skillet, or a casserole dish. Press the dough out to the edges of the pan. Cover, and let rest while you make the sauce.
Heat the oil in a medium pot over medium-high heat, and add the onions. Cook, stirring occasionally, until onions are softened, about 4 min. Stir in the squash and cinnamon, and season with salt and pepper. Continue to cook, stirring frequently, until the squash starts to soften, about 5 min. more.
Add 1 cup water to the pot, and bring to a simmer. Cook, stirring frequently, until the squash is creamy tender and the water is almost reduced, about 7 min. more.
Scrape the squash and any liquid into a blender or food processor, and add the yogurt. Pulse until smooth, about 1 min. Season with more salt and pepper if necessary. (There will be leftover sauce for 5 more pizzas. Store in the refrigerator for 5 days, or in the freezer for up to 3 months.)
Sprinkle the mozzarella over the pizza, going all the way up to the edges of the pan. Be generous with the cheese where the dough meets the pan. During the cooking process, the dough and cheese will caramelize against the high heat of the pan, creating the best part of Detroit-style pizza: the frico crust.
Spoon 1/2 cup squash puree over the center of the pizza, leaving a 1/2-in. diameter at the top of the crust uncovered. Sprinkle the olives over the puree. Then cover the pizza with the kale, and sprinkle with the pecorino.
Bake for 16 to 18 min., or until the edges are sizzling and golden brown and the kale is crisp. Run a butter knife around the edge of the pan to release the cheesy frico crust from the pan. Slice, and serve drizzled with chili oil and more pecorino.
Recipe by Emily Hyland, of Pizza Loves Emily in New York and Emmy Squared.