Preheat your oven to 200°C (390°F). Place the pumpkin halves cut-side down on a parchment-lined baking sheet and roast for about 45-50 minutes until the flesh is soft and caramelized with a fragrant aroma. Let cool slightly before scooping out the flesh into a bowl and mashing until smooth.
In a large mixing bowl or stand mixer, combine the flour and eggs. Mix or knead until the dough comes together into a smooth, elastic ball. Wrap in plastic wrap and let rest for at least 30 minutes to relax the gluten, making it easier to roll out.
Divide the rested dough into four pieces. On a lightly floured surface, roll out each piece into a thin sheet, about 1/16 inch thick, using a rolling pin or pasta machine. Keep the sheets covered with a damp cloth to prevent drying out.
Place small spoonfuls of the mashed pumpkin filling evenly spaced on one sheet of pasta, about 1 inch apart. Cover with a second sheet of dough and press around each mound to seal, then cut into individual ravioli using a fluted cutter or knife. Ensure the edges are well sealed to prevent filling from escaping during boiling.
Bring a large pot of salted water to a boil. Carefully drop the ravioli in and cook for 2-3 minutes until they float to the surface, signaling they are done. Use a slotted spoon to gently lift them out and set aside.
While the ravioli cooks, melt butter in a skillet over medium heat until it begins to brown and smell nutty, about 2-3 minutes. Add the sage leaves and fry until crispy, about 1 minute, then remove from heat.
Toss the cooked ravioli gently in the brown butter and sage mixture, coating them evenly. Plate the ravioli and drizzle with the remaining brown butter and crispy sage. Finish with a sprinkle of grated Parmesan if desired.
Serve immediately while warm, enjoying the tender pasta, sweet pumpkin filling, and aromatic brown butter with sage. A perfect seasonal dish that combines textures and deep flavors in every bite.
