Sift flour and salt onto a work surface.
Make a wide well in the center of the flour.
Crack the full egg in the well.
Add egg yolks and oil and gently whisk the wet mixture together within the well.
Slowly fold in the flour mixture, a little at a time, until the dough is too stiff to mix with a fork.
Using a bench scraper, cut into the mixture to break up the gluten, while continuously using your hands to bring the entire mixture together. Fold it into a single mass.
Knead the dough with your hands for 7-10 minutes, adding more flour as needed.
Form a ball with the dough and cover it, allowing it to rest for 30 minutes.
Roll the dough out into a ¼ inch thick rectangle (thin enough to fit into the KitchenAid Pasta Roller attachment at its widest setting).
Move the rollers to the next smallest setting and pass the dough through again. Continuously lower the size settings, passing the dough through once or twice each time.
Stop rolling with the dough is thin enough to partially see-through.
Cut the length of dough into 24-inch sections.
Lay out each section and working one pasta sheet at a time, lightly spray each sheet with water.
Starting on one edge, spoon out 2 teaspoons of filling in the center of each sheet, leaving 1 inch of space on each side.
Lift the top edge of the sheet and bring it over the top of the filling, lining it up with the bottom edge.
Using your fingers, gently press the dough as close as you can to the filling. Try to eliminate any air pockets that form.
Press again on the edge to seal it completely.
Using a fluted pastry wheel, trim the long edge of the pasta. Then cut in between each section to create the individual raviolis.
Bring a large pot of salted water to a rolling boil. Add raviolis to hot water, working in batches to not overcrowd the pot.
Cook for 3-4 minutes and then gently scoop out the raviolis, strain out any excess water and transfer to a plate.
Drizzle brown butter sauce over raviolis.
Top with extra grated parmesan cheese and chopped parsley.
Serve immediately.