Boil and eggs for ten to twelve minutes. Let cook and peel.
Cut six of the eggs in half and scoop out the egg yolks. Clean the egg white with a damp paper towel and place the egg yolks into the food processor.
Set the egg white onto a plate and place it in the fridge.
Add the remaining six hard-boiled eggs to a food processor with the egg yolks. Add the avocado, lime juice, grated white cheddar cheese, chopped celery leaves, smoked paprika, sea salt, and freshly cracked peppercorns.
Add a tablespoon at a time of EVOO until the mixture is smooth and creamy, and adjust the seasoning to taste.
Spoon half of a cup into a pipping bag or a small zip-lock plastic bag, and pipe in a dozen hard-boiled eggs white.
Dust the eggs with smoked paprika or Old Bay Seasoning, and sprinkle on sesame seeds.
Spoon the remaining dip into a small serving vessel and top with the chopped carrots, celery, radish, and celery leaves.
Drizzle with your favorite oil.
Serve.