For the sauce, combine the egg yolk, lemon juice, garlic, Dijon mustard, kosher salt, parsley and white pepper in a blender or food processor. Process until blended. Add the olive oil gradually, processing constantly until of a mayonnaise consistency.
For the dip, sauté the onion in the olive oil in a medium skillet until tender. Remove from heat. Place the artichokes in a large bowl, breaking up the artichokes slightly. Add the sauce, 1/3 cup parmesan cheese, asiago cheese, Romano cheese, garlic, white pepper and kosher salt and mix gently.
Spoon the artichoke mixture into a 1-quart baking dish. Sprinkle with 1/3 cup parmesan cheese. Bake at 450 degrees for 8 to 10 minutes or until golden brown. Cool slightly. Sprinkle with the basil. Serve with chips and/or assorted party crackers.