Preheat oven to 375 degrees. Bring a large pot of water to a rolling boil. Add sliced squash to a large rimmed baking sheet. Toss with olive oil. Sprinkle with brown sugar, salt, and pepper. Toss again. Spread the squash on the baking sheet. Roast until caramelized on one side, about 15-20 minutes. Turn over and roast another 5-6 minutes until caramelized and cooked through. Set aside.
While the squash cooks, add butter to a large skillet. Turn the heat on medium-high. Swirl the pan until the butter has melted. Once the butter starts to turn brown, continue to swirl the pan. Keep swirling until the butter is a deep brown and smells very nutty. Remove from the heat and add sage leaves. Return to the heat and fry sage until godlen brown and crisp, about 1 minute. Remove sage leaves and drain on paper towel. Remove the skillet from the heat and set aside.
Add ravioli to the boiling water. Cook according to package directions. Once the ravioli is about 1-2 minutes shy of being cooked, spoon 1/4 cup of the pasta water into the brown butter. Return the brown butter to a medium heat. Whisk in 2 tablepsoons of the parmesan cheese. Whisk until melted.
Use a slotted spoon to scoop the ravioli out of the boiling water and into the brown butter sauce. Gently toss. Season with salt and pepper.
Add squash, fried sage, and walnuts to the ravioli. Toss again, gently. Season one more time with salt and pepper. Garnish with remaining grated parmesan.