1. Put the flour, eggs, oil, and salt into a food processor. Pulse until the dough begins to form a mass, about 2 minutes.
2. Transfer the dough to a lightly floured surface and knead until the dough is elastic and smooth, about 5 minutes. Cover with plastic wrap; let rest 30 minutes.
3. To make the pesto, combine the arugula, parsley, walnuts, cheese, garlic, lemon zest, lemon juice, olive oil, and salt in a food processor and process until smooth. Transfer to a bowl. Cover and refrigerate until ready to use.
4. To make the filling, combine the ricotta, prosciutto, smoked Gouda, Parmesan, parsley, and egg in a large bowl. Cover and refrigerate until ready to use.
5. To make the tortellini, cut the dough into 4 equal pieces. Keep unused dough covered in plastic wrap while working with one piece. On a well-floured surface, with a floured rolling pin, roll out one piece of dough to
1/8-inch thickness. With a 2 1/2-inch cookie cutter, cut dough into 12 rounds.
6. Place a scant teaspoon of filling in the center of each round. Lightly moisten the edges with a pastry brush dipped in water. Fold the top of the round over the filling to make a half-moon. Pick up both corners and bring them toward each other. Tuck one corner behind the other and press together. Place the tortellini on a baking sheet lined with a clean, lightly floured kitchen towel. Repeat with the remaining dough and filling. You should have a total of about 48 tortellini.
7. At this point, tortellini can be frozen and transferred to a zipper-close freezer bag for up to 3 weeks.
8. To cook the tortellini, bring a large pot of salted water to a boil. Add the tortellini, in batches, and cook until the tortellini begin to float to the surface, about 3 minutes. Drain; transfer to a large bowl. With a rubber spatula, gently toss the tortellini with the pesto until lightly coated. Serve at once.