1 medium butternut squash, halved lengthwise and seeded
2 teaspoons olive oil
½ teaspoon kosher salt, plus more to taste
One 12-ounce package jumbo pasta shells
1 cup whole-milk ricotta cheese
1 cup grated Parmesan cheese, divided
1 egg, lightly beaten
1 large garlic clove, finely chopped and smashed
3 tablespoons chopped flat-leaf parsley
4 teaspoons fresh lemon juice (juice of ½ lemon)
2 teaspoons finely grated lemon zest
2 teaspoons chopped fresh oregano
Two 8-ounce or four 4-ounce burrata balls
1. Preheat the oven to 400° and line a sheet tray with parchment paper.
2. Place the squash onto the prepared sheet tray and season the flesh with the olive oil and salt. Turn them so that they're cut-side down and roast until tender, 35 to 40 minutes. Let cool for 7 to 10 minutes, then scoop the flesh into a medium bowl and set aside. Lower the oven to 375°. Yields about 3 cups. Make ahead: The squash and can be roasted and stored in fridge for up to 2 days.
3. While the squash is roasting, boil the pasta: Bring a large pot of salted water to a boil. Add the jumbo shells to the water and cook until barely al dente, 9 minutes. Drain the pasta and rinse under cold running water for 1 minute.
4. In a large bowl, combine the ricotta, ¾ cup of the Parmesan, the egg, garlic, parsley, lemon juice and zest, oregano and cooled roasted squash. Taste and adjust the seasoning with salt. Fill each cooked pasta shell with 1½ tablespoons of filling and snuggle the shells into a 9-by-13-inch baking dish.
5. Tear the burrata over the pasta, letting the curds and cream fall over and around the shells. Top with remaining Parmesan and bake until golden brown and bubbling, 30 minutes. Serve.