Preheat the oven to 400°F. Line two baking sheets with parchment paper.
Slice the eggplant into 3/8 to 1/2-inch slices. In a small bowl, combine the olive oil and paprika. Place the eggplant slices on the baking sheets, splitting them evenly between the two sheets. Brush each side of the eggplant slices lightly with the paprika oil (if you need more oil at the end, add a another drizzle and stir in the remaining paprika). Season all of the eggplant liberally with kosher salt and several grinds of black pepper.
Slide the trays into the oven and bake for 10 minutes. Flip the eggplant slices, then reverse the trays and finish baking for 5 minutes or until tender.
In a large, ovenproof skillet, spoon a bit of the marinara sauce and spread in an even layer. Add an even layer of half of the eggplant slices, a bit of sauce, then half of the mozzarella and feta cheese. Add another layer of eggplant, then more sauce, then the remaining mozzarella cheese. Top with the remaining feta.
Bake for 20 minutes until the cheese is melted and bubbling. Garnish with parsley and serve.