PASTA

In a medium-sized bowl, combine the flour and salt. Transfer the mixture onto a clean work surface, creating a well in the center. Crack the eggs into the well and gradually whisk in the flour using a fork until a shaggy dough forms. Knead the dough by hand until smooth and no longer sticky, roughly 5 minutes. Sprinkle the surface with additional flour as needed to prevent sticking. Wrap the dough in plastic wrap and refrigerate for a minimum of 1 hour.

When the dough is ready, cut it into quarters, keeping three pieces wrapped while working with one.

On a lightly floured surface, roll out the dough into a long rectangle about 1/4 inch thick. Adjust your pasta machine to the widest setting and feed the dough through twice. Fold the short edges of the dough into the center, then fold in half, resulting in four layers. Roll the dough again to 1/4 inch thickness, then pass through the machine two more times.

Decrease the setting by one notch and repeat the folding and rolling process 2 to 3 times before adjusting to the next setting. Continue until you reach the thinnest setting, cutting the pasta sheet in half if it becomes too long. Repeat with the remaining dough. Cover the rolled sheets with a clean kitchen towel to prevent drying out.

FILLING

In a large bowl, blend together the butternut squash purée, Parmesan, ricotta, and brown sugar. Add salt and pepper to taste, ensuring a balanced flavor.

SAUCE AND ASSEMBLY

On a lightly floured surface, place one sheet of pasta. Spoon about 1 tablespoon of the filling every inch along the sheet. If the pasta is wide enough, create two rows of filling. Lightly dampen the spaces between the filling mounds with water using your finger. Lay a second sheet of pasta over the top and gently press around each filling mound to seal, removing any air pockets. Use a pasta cutter or a pizza wheel to cut the ravioli into individual pieces. Repeat with remaining dough and filling. Keep in the refrigerator until ready to cook.

Heat a large skillet over medium heat and melt the butter until it becomes foamy. Lower the heat to medium-low and continue cooking until the butter turns a deep golden hue and releases a nutty aroma, about 4 minutes. Stir in the minced garlic, sage, and thyme, cooking until fragrant, roughly 1 minute, then remove the skillet from heat.

Bring a large pot of salted water to a boil. Working in batches, add the ravioli and cook until tender, approximately 1 1/2 minutes. Use a slotted spoon to transfer the cooked ravioli directly into the browned butter sauce, gently tossing to coat