Slice the onions and cook them in butter over medium heat until they are caramelized, about 40 minutes.
In a blender, combine the caramelized onions, olive oil, egg yolks, grated Parmesan cheese, water, salt, and pepper.
Blend until smooth. Add more water to thin it out a little if needed.
Add the water in parts throughout the blending process.
Toss the cooked pasta with the sauce in a large pan.
Warm over low heat for about 1 minute, then turn off the heat.
Garnish with fresh parsley if desired.
