1. Blend the flour, egg yolks, oil, 5 tablespoons water, and 3/4 teaspoon salt in a food processor until a dough forms. Let the dough rest, wrapped in plastic, for 1 hour. Cut the dough into quarters and dust with flour. Roll the dough using a pasta maker on the widest setting 8 times, folding dough each time and flouring in between. Continue rolling the pasta on the narrower settings, without folding, until the second narrowest setting. Place the dough on a floured counter covered with a towel. Repeat with the remaining dough.
2. Pulse 1/2 cup walnuts, the ricotta, lemon zest, and 1/2 teaspoon each salt and pepper in a clean food processor. Place 1 teaspoon of filling 1 1/2 inches apart along 2 pasta sheets. Brush the edges and between the mounds with water, and then top with another pasta sheet, pressing around the filling to seal. Cut out square ravioli, about 30, with a sharp knife and transfer to a floured towel.
3. Heat the butter in a large, heavy skillet over medium-high heat until the butter begins to brown, 4 to 6 minutes. Remove from the heat and stir in the garlic, lemon juice, the remaining 1 cup walnuts, 1/2 teaspoon salt, and 1/2 teaspoon pepper. Reserve the sauce.
4. Boil the ravioli in a large pot of boiling salted water until tender, about 3 minutes. Gently transfer the ravioli with a slotted spoon to a bowl with the sauce, arugula, and Parmesan. Toss to combine, then divide among warmed serving plates.
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