Make the pasta dough: Mound the flour on a clean work surface and make a well in the center. Add eggs, olive oil, and salt. Whisk with a fork, gradually pulling in flour from the edges, until a shaggy dough forms.
Knead for 8–10 minutes until smooth and elastic. If sticky, dust with a little flour; if dry and cracking, dampen your hands and continue kneading. Wrap tightly and rest at room temperature for 30 minutes.
Make the pumpkin filling: In a bowl, mix pumpkin puree, (optional) mashed roasted butternut squash, Parmesan, egg yolk, nutmeg, salt, and pepper until thick and smooth. Cover and refrigerate while you roll the dough.
Roll the pasta: Divide dough into 4 pieces (keep covered). Roll one piece into a rectangle. Using a pasta machine, pass through gradually thinner settings until the sheet is very thin (you should almost see your hand through it). Dust lightly with flour as needed. Repeat with remaining dough.
Fill and shape the ravioli: Lay one pasta sheet on a floured surface. Dollop 1–1½ teaspoons filling every 2 inches. Brush a little water around each mound. Lay a second sheet over the top and press around each mound to remove air and seal.
Cut into squares with a ravioli cutter, fluted wheel, or knife. Press edges firmly (crimp with a fork if you like). Transfer to a floured tray and cover with a towel while you finish shaping.
Cook the ravioli: Bring a large pot of well-salted water to a gentle boil. Cook ravioli in batches for 3–4 minutes, or until they float and the pasta looks slightly puffy. Remove with a slotted spoon (don’t drain in a colander—fresh ravioli are delicate).
Make the sage brown butter: While ravioli cook, melt butter in a large skillet over medium heat. (Optional) Add garlic and cook 30–60 seconds. Continue cooking until butter turns golden and smells nutty, then add sage and cook until sage is crisp, 30–60 seconds.
Toss and serve: Add cooked ravioli to the skillet and toss gently to coat. Serve immediately with extra Parmesan and (optional) toasted pecans on top.