In a blender, puree the olive oil, 1 cup of the basil, and ¼ teaspoon salt until smooth. Set aside.
Divide the stuffed grape leaves, Feta, cucumber, tomatoes, pepperoncini, lemon, olives, and remaining ½ cup of basil among plates.
Season the tomatoes and cucumbers with ¼ teaspoon each salt and pepper. Drizzle with the basil oil before serving.