For the dough: In the bowl of a stand mixer fitted with a paddle attachment, or on a work surface, add the flour and make a well in the center. On medium speed, or using your fingers, mix in the egg yolks, oil and 1 tablespoon water, adding them one ingredient at a time and mixing just until the dough comes together, 2 to 3 minutes. If the dough seems dry, add another tablespoon of water.
Knead in the mixer on medium speed for 4 to 5 minutes, or turn the dough out onto a lightly floured work surface and use the palms of your hands to knead the dough until it feels silky and smooth, 8 to 10 minutes.
Shape the dough into a ball, cover the dough with plastic wrap and let it rest at room temperature for at least 30 minutes or in the refrigerator for up to 5 days.
To roll the dough, cut it into 4 equal pieces. Let the pieces sit, covered, at room temperature for 10 minutes if chilled.
Shape each piece into an oval wide enough to fit the width of your pasta roller. Lightly flour your work surface and set the pasta roller to its widest setting. Lightly flour one piece of dough, pass it through the roller and then lightly dust the rolled dough with flour, brushing off the excess with your hands. Pass the dough through the widest setting again. Lower the setting by 1 notch and continue to pass the dough through until you've reached the desired thickness. The thinner the better in my opinion.
For the filling: Combine the ricotta, pesto and egg in a medium bowl.
Form the ravioli with 1 tablespoon of filling in each. You can make them with a tray mold, stamp or by hand, with many options for shapes and sizes.
Place the ravioli on a baking sheet lined with a kitchen towel or parchment paper that has been dusted with flour to prevent them from sticking. Dust the raviolis on top with flour as well. Continue the process with the remaining dough sheets and filling. They can all be frozen at this point
Bring a pot of water to a boil and salt liberally. Drop in the ravioli and cook for 4 to 5 minutes.
For the sauce: Meanwhile, heat a large pan over medium heat, add the butter and cook until melted and golden brown, 4 to 5 minutes. Add the peas if using and 1/2 cup of the pasta water and bring to a simmer. Transfer the ravioli to the pan and shake the pan to coat them in the sauce. Remove from the heat and add the Parmesan.
For more ingredient substitution ideas, see the article below.