Bring a large pot of water to a boil, salt it, add the pasta and cook until al dente. Drain, reserving about 1/2 cup of the pasta cooking water.
Meanwhile, pat the fish dry and season with salt, pepper and a little Old Bay. On a plate, mix the flour and cornstarch. Coat the fish in the flour mixture.
In a large skillet, heat 1 tablespoon EVOO, 1 turn of the pan, over medium-high heat. Add 2 tablespoons butter and let it foam up, then add the fish fillets and cook, turning once, until golden-brown and firm, 4 to 6 minutes. Transfer the fillets to a plate and cover with foil to keep warm. Wipe out the pan and return to the heat. Add 1/2 tablespoon EVOO, 1/2 turn of the pan, and the remaining 2 tablespoons butter to melt. Stir in the garlic for 1 minute, then stir in the wine for another minute. Add 1 teaspoon grated lemon peel and the juice of 1 lemon. Thinly slice the remaining lemon and stir the slices into the sauce, along with the capers and parsley. Spoon the sliced lemons and half of the butter sauce over the fish.
Add the reserved pasta water and the pasta to the skillet. Add the remaining butter sauce and season with salt and pepper; toss. Transfer the pasta to a platter. Add the remaining 1/2 tablespoon EVOO, 1/2 turn of the pan, to the skillet. Add the spinach, season with salt, pepper and the nutmeg and cook to wilt. Serve the fish with a little pasta and spinach alongside.