Remove top of banana pepper, core and seed it, then cut lengthwise into slices. Place on a baking sheet and brush with olive oil.
Broil on each side until skin is lightly browned (about 2’5 minutes). Remove skin from pepper and discard.
In a food processor, combine the peppers, feta cheese, and olive oil. Blend until a smooth but thick texture is obtained. Refrigerate until ready to serve.