Preheat broiler. Place cherry peppers on a rimmed baking sheet and roast in broiler until skins are charred and peppers are softened, turning peppers as necessary to roast evenly.
Transfer peppers to a bowl, cover with plastic wrap, and let sit until cool enough to handle, about 15 minutes. Peel, stem, and de-seed peppers.
Place peppers in the workbowl of a food processor fitted with a steel blade. Add in feta, yogurt, olive oil, and lemon juice.
Puree until peppers and feta are as smooth as possible and sauce is completely combined.
Transfer to a bowl and serve with warm pita.
