Place the feta in a food processor and process until smooth. With the machine running, add the olive oil to make a very smooth and creamy spread. Add the lemon juice, zest, mint, and pepperoncini and pulse to combine.
Transfer the whipped feta to a decorative serving bowl and refrigerate it, covered, for a few hours to firm it up. Serve the feta on a platter surrounded by the dippers of your choice.