Add the diced butternut squash, chopped onion, whole garlic cloves, olive oil, salt, and pepper to a baking sheet, tossing until fully coated. Bake until the squash is golden brown and tender, about 30 minutes.
While the squash is in the oven, get your dough ready. When the squash is finished cooking, add it to the food processor along with the brown sugar, garam masala, nutmeg and Parmesan cheese. Pulse until it becomes smooth. Set aside to chill.
Lay a sheet of pasta on a lightly floured countertop. Place a tablespoon of the butternut squash filling at 2-inch intervals and place a second sheet on top of the first sheet, being sure to gently press around each mound of squash. Use a pasta cutter to cut between the mounds and form your raviolis. Alternately, use a round ravioli cutter to cut out individual round raviolis.
Gently place a few raviolis into boiling salted water and cook until the raviolis float and firm up slightly, 2-3 minutes. Scoop out the ravioli and set aside briefly to cook a new batch or dump out the water and start the hazelnut brown butter sauce.
In a large sauté pan, add 3 tablespoons of the butter, sage leaves, and hazelnuts. Cook until the butter browns deeply, the nuts are heated through, and the sage is fried and crispy. Turn down the heat to low and add the lemon juice and season to taste.
Swirl in the remaining 2 tablespoons of chilled butter, to thicken the sauce. Add the cooked raviolis to the pan and toss gently to coat the pasta.
