Place dill, mint, parsley, basil, garlic, scallions, lemon juice and salt in a food processor and process until finely chopped.
With motor running, drizzle in the olive oil until incorporated. Add feta and process until smooth; pulse in yogurt. Taste dip and add more salt, if desired. If you like a creamier, richer dip, add mayonnaise and pulse to combine.
Serve dip immediately with vegetables or pita chips or cover and store in refrigerator for up to 3 days. This also makes a great sauce for cooked vegetables or fish.