For the chili: Heat the oil in a 12-inch cast-iron skillet over medium-high heat. Add the squash and a pinch of salt and black pepper and cook, stirring occasionally, until the squash is tender and browned in spots, about 8 minutes. Remove the squash from the pan and set aside.
Reduce the heat to medium. Add the garlic and onion and cook, stirring often, until the onion is soft, about 8 minutes. Add the chili powder (use less if you like milder chili) and cumin and cook until fragrant, about 1 minute. Add the vegetable stock, tomatoes, beans, sugar and cooked squash and bring to a simmer. Cook until all of the vegetables are tender and the sauce has thickened, about 30 minutes. (If the liquid reduces to less than three-quarters of the way up the sides of the squash, stir in a little water.) Stir in the baby spinach by the handful until all is incorporated and wilted.
For the cornbread topping: Meanwhile, position a rack in the center of the oven and preheat to 400 degrees F. Whisk the cornmeal, flour, baking soda, sugar and 1 teaspoon salt together in a medium bowl. Whisk the milk, sour cream and egg together in another bowl. Add the wet ingredients to the dry ingredients, whisking until well combined. Stir in the melted butter and Cheddar. Drop spoonfuls of the batter on top of the chili, leaving space in between. (The batter will not completely cover the chili.)
Bake until the cornbread is golden brown and springs back when touched and the chili is hot and bubbly, about 18 minutes. Serve with more sour cream and pickled jalapenos.
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