- Preheat an oven to to 400°F. Line a rimmed baking sheet with parchment paper.
- Cut the pumpkin in half lengthwise, discarding the stem. Scoop out the seeds and discard. Peel the pumpkin halves and cut the flesh into chunks. Place on the prepared baking sheet and bake until very soft when pierced with the tip of a knife, about 25 minutes. Let cool to the touch, then put into a food processor. Process the roasted pumpkin until smooth. Add the egg yolk and cheese and pulse to blend. Season with salt, pepper and nutmeg and pulse to combine. Set aside.
- Lightly flour 2 rimmed baking sheets.
- Make the pasta dough according to the recipe, then divide and roll out each piece into a sheet 1/16 inch thick, as directed in the related tip at left. Trim each pasta sheet into long, 2 1/4-inch-wide strips that will fit on one of the prepared baking sheets. Layer the strips on the sheet, spacing them so they don’t touch and separating each layer with a lightly floured kitchen towel.
- To make the tortelli, place a pasta strip on a floured work surface. Use a 2-inch round pastry cutter to make pasta circles. Place 1 tsp. filling in the center of half the circles. Lightly brush a little water around the filling, top with the remaining circles and press the edges to seal. Repeat with the remaining strips.
- Place the filled tortelli in a single layer on the second prepared baking sheet, separating each layer with a lightly floured kitchen towel. Keep the top layer covered as you prepare the remaining tortelli. They will keep, refrigerated, for up to 3 hours before cooking.
- To make the sauce, in a large fry pan over medium heat, melt the butter. Cook, swirling the pan, until the butter foams and begins to brown. Add the sage and cook until the leaves crisp slightly and the butter turns nut brown, about 3 minutes. Be careful not to burn the butter. Remove from the heat and cover to keep warm.
- Meanwhile, bring a large pot three-fourths full of water to a rolling boil. Add the 2 tablespoons salt and then the tortelli and stir gently. Cook, stirring occasionally and adjusting the heat so the water simmers gently, until the tortelli rise to the surface and are al dente, 3 to 4 minutes.
- Return the fry pan with the sauce to low heat. Using a large slotted spoon, transfer the tortelli to the sauce and toss gently to coat. Divide among warmed plates and serve immediately.