Preheat a large nonstick skillet over medium to medium high heat. Season the fish with salt and pepper. Beat eggs with cream. Add 2 tablespoons extra-virgin olive oil to the skillet, 2 turns of the pan then add 2 tablespoons butter, cut into small pieces. Dip the fish into the eggs and cook on both sides until just golden, 5 to 6 minutes total. Transfer fish to a plate and cover with loose a foil tent to retain heat.
Add wine to the pan and reduce by half, 1 minute, then add 1 tablespoon butter and a handful of parsley to the pan. Stir in the lemon juice and zest and the capers. Turn off heat. Pour sauce over fish and top with sliced almonds.
Return skillet to heat. Add remaining 2 tablespoons extra-virgin olive oil, 2 more turns of the pan. Add chopped garlic and let it speak by coming to a sizzle. Wilt in spinach, turning to coat in extra-virgin olive oil and season with salt, pepper and nutmeg. Serve spinach alongside flounder.