Place the flour in a shallow dish and season with the garlic and Old Bay (or paprika). In a second shallow dish, beat the eggs with the juice of 1 lemon and the cheese.
In a large skillet, heat about 3 tbsp. EVOO, 3 turns of the pan, over medium to medium-high heat. Season the sole with salt and pepper; dip 2 fillets in the flour, then coat evenly with the egg-cheese mixture. Saute the sole until deep golden, 3 to 4 minutes on each side; transfer to a warm oven. Repeat with remaining fillets.
In a bowl, combine the arugula and tomatoes and use a vegetable peeler to add some shaved curls of parmigiano-reggiano. Dress the salad with the juice of 1 lemon and the remaining EVOO; season with salt and pepper.
Serve each fillet with a wedge of lemon and some salad.