Slice the onions and cook them in butter over medium heat until 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, adding water in parts throughout the blending process to achieve desired consistency
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 and serve
