Prepare the ravioli dough. Pour the flour onto a clean work surface, creating a well in the center. Crack the eggs and pour into the well. Using a fork, carefully whisk the eggs, slowly dragging in the flour into the well. Continue to whisk until the flour and eggs are incorporated. Knead the dough for 10 minutes or until the dough is smooth and elastic. Cover and let rest for at least 30 minutes at room temperature.
Meanwhile, prepare the filling. Place the butternut squash in a medium pot. Fill with enough water to cover the squash, cover the pot and bring to a boil over high heat. Reduce to a simmer over medium heat and cook for 15 minutes or until squash is fork tender. Drain. Mash butternut squash until smooth.
Heat 1 tablespoon butter in a saute pan over medium heat. Add shallots and cook until translucent, about 1 minute. Add the squash and cook until slightly dry, about 2-3 minutes. Remove from heat and stir in heavy cream and ricotta. Season with salt and pepper. Set aside and let cool.
Prepare the parmesan broth. Heat 1 tablespoon oil in a medium pot. Add onion and garlic and cook until browned, about 5 minutes. Add parmesan rind and vegetable broth. Bring to a boil. Reduce heat and simmer for 20 minutes. Strain broth, discarding rind, onion, and garlic. Bring back to heat and add heavy cream and parmesan. Season with salt and pepper.
Prepare the ravioli. Using a pasta machine, roll out the dough until it is ⅛ inch thick. Start by rolling out the dough at the thickest setting 6-8 times. Move the machine up one notch and repeat. Repeat once more at the 3rd setting. At the fourth setting, roll the dough 1-2 times. Continue to move up the settings until you have the desired thickness.
Heavily flour the ravioli press. Lay one sheet of dough on top, making sure to cover the entire mold. Place about 1 tablespoon filling in the center of each ravioli. Lay another layer of dough on top. Roll a rolling pin over the mold to seal the edges. Flip the mold over and gently tap on the counter to remove the ravioli from the press. Using a knife or pizza cutter, cut the ravioli into individual pieces. Lay the ravioli on a baking sheet coated with flour. Cover and repeat with remaining dough and filling.
Bring a large pot of salted water to a boil. Boil the ravioli for 2-3 minutes or until they float to the top.
Remove ravioli from the water with a slotted spoon into the sauce. Toss to coat. Portion on to plates and finish with more parmesan. Serve immediately.