In a large pot, cook pasta in well salted water (I usually add about 2 tablespoons of salt to the water) according to package directions, until al-dente. 

While pasta is cooking, place the hardboiled eggs in a small bowl and “mash” them in a bowl with a fork into small pieces. Set aside. 

In a food processor or blender, finely grate the onion and then add the olive oil. Set aside. (You can also finely grate the onion by hand with a cheese grater and then stir to combine with the olive oil.)

In a medium sized bowl, combine the mayo, mustard, salt and white pepper, whisking until well combined. Set aside. 

Once pasta is done cooking, drain the pasta and transfer it to a large mixing bowl and add the butter. (The heat from the pasta will melt the butter.) Stir the pasta until butter is melted and is coating the pasta. 

Add the mayo sauce and onion/olive oil mixture to the buttered pasta and mix until well combined. Then fold in the mashed hard boiled egg. 

You can serve it immediately, but I recommend refrigerating it for at least 4 hours before serving.