Preheat the oven to 400 degrees F. Wear gloves when you are handling hot peppers. Arrange the long peppers and chili peppers on a baking sheet until the skin is dark and blistering, about 25 minutes. If you don’t bake them long enough, the skins will be difficult to remove.
Using your hands, rub the skins to remove them. Then cut the peppers in half lengthwise and remove the seeds and the stem. Blot the peppers dry with a towel.
Transfer the peppers to a food processor. Add the feta, vinegar, olive oil, and yogurt. Pulse the processor until the mixture is smooth.
The Greek cheese dip can be refrigerated and covered in an airtight container for 3 to 4 days.