Preheat the oven to 400ºF.
Cut pumpkin in half, scoop out the seeds and discard.
Drizzle about a teaspoon of olive oil on a baking sheet.
Season inside of pumpkin with salt and place cut side down. Roast for about 45 minutes or until a knife inserts easily through the skin into the flesh.
Remove from the oven and let cool completely.
Scoop out flesh and place in a bowl.
Add the two cups of cheese and season with salt to taste. Mix to combine. Taste and add more salt until the mixture tastes well seasoned.
Add the eggs and mix to combine. Set aside.
Mound flour in the center of a medium-sized bowl.
Make a well in the center of the mound of flour.
Add the eggs to the center. Using a fork, beat the eggs and begin to incorporate the flour, starting with the inner rim of the well.
When the eggs are almost completely incorporated, start kneading the dough in the bowl and then transfer to a large, lightly floured wooden board and continue to knead for 10 minutes, dusting the board with additional flour as necessary.
The dough should feel elastic and a little sticky. Wrap the dough in plastic wrap and allow to rest for 30 minutes at room temperature before using.
Divide the dough into 4 pieces.
Keep the dough covered with plastic wrap at all times. â€¨Lightly flour one of the pieces of dough, and shape into a rectangle about ½-inch thick.
Pass through the widest setting on a pasta machine. Fold the dough in three, like a letter, and pass through the same setting again feeding the short end in first. Repeat this step 2 times, adding flour as needed.
Without folding the dough now, repeatedly pass it through the machine rollers, reducing the space between the rollers after each pass. When it has passed through the thinnest setting, it is ready to be shaped into ravioli. (If the dough gets too long and difficult to deal with, cut it in half and feed each piece through separately until each has passed through the thinnest setting).
The dough should be just less than 6 inches wide. On the bottom half of the dough, place heaping teaspoons of the squash filling, evenly spaced every 1½ inches. Fold top half of dough over bottom half. With a knife or fluted roller, cut between each mound to create the individual raviolis.
Gently pinch to seal the two dough layers together, using a tiny bit of water if necessary. Transfer to a baking sheet dusted with flour and cover with plastic wrap while you shape the remaining sections of dough.
At this point, decide how many ravioli you want to cook, and then freeze any remaining: Do not store ravioli in the refrigerator — they become a soggy mess.
Bring a large pot of water to a boil and add 1 tablespoon of salt.
Place butter in a small sauté pan and heat until it bubbles.
Add the sage leaves and let sizzle until crisp, about 1-2 minutes total. Turn off the heat, remove leaves with tongs and drain on a paper towel. Set aside.
When water boils, add ravioli and cook until tender about 2-3 minutes (frozen ravioli also take only about 3 minutes). When ravioli are done, drain, or remove with a spider, but do not rinse under cold water.
Place ravioli on a serving platter. Heat butter again until hot and begins to brown. Return the sage leaves and then spoon brown-butter over ravioli. Sprinkle with cheese.