Process the fresh ingredients in a food processor. Put the dill, mint, parsley, and basil in a food processor. Add the garlic, scallions, lemon juice, and a pinch of sea salt. Process the ingredients until they are finely chopped.
Add the remaining ingredients one at a time. With the motor running, drizzle in the extra virgin olive oil until it is incorporated into the mixture. Add the feta cheese and process the mixture until it is smooth. Add the yogurt and pulse. Add the mayonnaise and pulse. Taste the dip and add more salt if necessary.
Serve the dip with an assortment of fresh vegetables.
