Combine the dill, mint, parsley, basil, garlic, green onions, lemon juice and salt in the bowl of a food processor and pulse until finely chopped.
With the motor running, drizzle in the olive oil. Add the feta and process until smooth; pulse in yogurt. Taste and add more salt, if desired. If you like a creamier, richer dip, add the mayonnaise.
Serve immediately with veggies or pita chips, or refrigerate for up to 4-5 days. (The flavour improves with some time in the fridge.)