Slice eggplant lengthwise. Brush all sides with olive oil, placing halves upside down on a baking sheet. Bake for 25 minutes.
Brush onion, garlic, and red pepper with oil; add it to the eggplant halves and continue to bake for another 25 minutes or longer until the vegetables are tender.
Cool the eggplant; scoop out the flesh and place in a food processor or bowl. Set aside.
Squeeze garlic pulp from skins, peel red pepper, and add them to the eggplant along with the onion, oregano, lemon juice, olive oil, salt, and pepper.
Process slightly or finely chop by hand, but do not puree.
Mix half of the feta cheese into the mixture and spoon it into a serving bowl or platter. Sprinkle the remaining feta around the edge of the mixture and garnish with fresh parsley.