Preheat the oven: Preheat your oven to 425°F and line a baking sheet with parchment paper. Bring a large pot of salted water to a boil.
Prepare the squash: Cut each honeynut squash in half lengthwise and scoop out the seeds. Lightly coat the cut sides with olive oil and season with salt and freshly cracked black pepper.
Roast: Place the squash flesh-side down on the prepared baking sheet. Roast for approximately 30–45 minutes, or until the flesh is tender and easily pierced with a fork.
Make the purée: Let the squash rest for 5 minutes. Scoop the flesh into a blender, add a drizzle of olive oil and a few tablespoons of chicken broth or water, and blend until completely smooth. Set aside.
Render the Guanciale and Brown the Butter
Cook the guanciale: Add the cubed guanciale to a cold skillet. Cook over medium-low heat for 8–12 minutes, allowing the fat to slowly render until the guanciale becomes deeply golden and crispy.
Reserve the fat: Remove the crispy guanciale with a slotted spoon and transfer it to a paper towel-lined plate. Reserve the rendered fat, leaving approximately 1 tablespoon in the skillet.
Toast the pepper: Add a generous amount of freshly cracked black pepper to the skillet. Allow the pepper to toast in the warm guanciale fat.
Brown the butter: Add 3 tablespoons of butter and the fresh sage leaves. Cook gently until the butter browns and develops a nutty aroma. Remove the crispy sage leaves and set aside for serving.
Cook the pasta: While the butter browns, add the mezzi rigatoni to the boiling salted water. Cook until approximately 3 minutes shy of al dente.
Emulsify the brown butter: Carefully add a ladle of hot pasta water to the skillet with the brown butter. Stir or toss until the butter and water begin to emulsify.
Add the pasta: Transfer the pasta directly to the skillet. Toss until the mezzi rigatoni is evenly coated in the brown butter sauce.
Add the squash: Add the roasted honeynut squash purée and a splash of pasta water. Continue tossing until the pasta is fully coated.
Finish with mascarpone: Add the mascarpone and some of the reserved crispy guanciale. Toss until the sauce becomes smooth and glossy. If the sauce is too thick, add more pasta water a few tablespoons at a time.
Serve: Plate the pasta and finish with the remaining crispy guanciale, fried sage leaves, and freshly grated Parmigiano Reggiano. Enjoy!