In the bowl of a food processor, combine the chèvre, 4 tablespoons yogurt, lemon zest or preserved lemon, lemon juice, red pepper flakes, pepper, and sea salt. Blend until smooth. Taste, and sea salt and up to 2 tablespoons yogurt, as needed. Pulse in the parsley.
Spoon into a container with a tight fitting lid and refrigerate.
Dip can be made up to three days ahead. Allow dip to come to room temperature and add garnishes before serving.