Heat oven to 400 degrees. Remove any stems from the squash using a paring knife. Hold a pattypan squash on its side and slice down the middle along its scalloped edges as you would with a bagel. Do the same to the other squash so that you have 4 squash “bowls.” Leaving a quarter-inch border, scoop out the halves with a spoon; chop and reserve the insides. Place the squash halves, skin side down, in a shallow baking dish. Season with salt and pepper, and set aside.
In a large pan, heat oil over medium-high heat. Add the chopped squash insides, onion, and garlic; season with sea salt and pepper. Cook, stirring occasionally, for a couple of minutes. Add the tomato paste and chili powder and cook, stirring, for an additional minute. Add the beef, breaking it up with a spoon and cooking until it’s no longer pink, about 2 to 3 minutes. Remove the pan from the heat and stir in the peppers, corn and Parmesan, if using; season with sea salt and pepper.
Spoon the beef mixture equally into each squash half. Sprinkle with extra Parmesan, if you like. Cover the baking dish with foil and bake until squash is tender, 15-20 minutes. Remove foil and bake until top is golden brown, 5 to 10 minutes more. Drizzle with yogurt and serve.