Cook the pasta. Bring a large pot of water to a rapid boil. Season generously with a couple tablespoons of Kosher salt, then add the pasta. Cook according to package directions until al dente. Before draining, reserve about ½-1 cup of the cooking liquid. Drain the pasta over a colander. While the pasta cooks, make the sauce.
Make browned butter. Add 4 Tbsp of unsalted butter to a large pan with deep sides set over medium heat. Cook, stirring occasionally, until the butter turns foamy and is a deep golden brown color, about 3-5 minutes.
Add the pumpkin. To the browned butter, add ½ cup canned pumpkin purée. Cook, stirring occasionally, until well mixed and homogenous, about 3 minutes.
Add the pasta. To this, add the cooked, drained pasta, ½ cup mascarpone cheese, ¼ cup grated Parmesan, 2 Tbsp chopped sage leaves, a pinch of ground cinnamon, and about ½-⅔ cup of the reserved pasta water. Adjust the heat to medium, then stir until very well mixed.
Stir in egg yolks. Turn the heat off, then add 2 large egg yolks to the pasta and stir vigorously to incorporate into the sauce. Taste, adjust seasoning, adding Kosher salt as needed, then transfer to serving bowls. Drizzle each with a little high-quality extra virgin olive oil and a generous pinch of flaky sea salt. Top with lots of freshly cracked black pepper and additional grated or shaved Parmesan. Enjoy!