Dredge the cheese slices in flour, tap off any excess. Chill while oil heats.
In a large non-stick skillet, heat oil over high heat, add the cheese slices and saute until golden brown on all sides, about 1 1/2 minutes on each side. Keep warm in oven while finishing next batches. Transfer cheese to platter, season with pepper, sprinkle with parsley, and finish with squeeze of lemon.