Dry the filets by blotting with paper towels, then season the flesh side with salt and pepper.
Combine the all-purpose and almond flours in a pie plate and dredge the fish on both sides, shaking off any excess. Place on a wire cooling rack and rest for 10 minutes. When the 10 minutes are up, dredge the fish again and return to the rack.
Park a 12-inch saute pan over medium-high heat for 2 minutes. Add 2 tablespoons of the butter and swirl the pan to evenly coat.
Hold the end of the filet(s) with the skin side facing you and carefully lay it flesh-first into the butter, making sure to lay it away from you so that the filet blocks any splattering butter. Give the pan a few jiggles to ensure the fish doesn't stick. Cook for 2 minutes, gently shaking the pan every now and then, until a golden crust forms.
Carefully flip the filets away from you with a fish turner or any flexible, slotted spatula, and give the pan another jiggle. Continue to cook until the skin is browned and crisp, about 2 minutes more. Remove to a plate.
Reduce the heat to low and add the capers to the pan, shaking constantly for 1 minute or until they start to brown.
Carefully add the wine. (If the pan is really hot and you're cooking on gas, this is a potential flambe moment!) Follow with the lemon juice, and 1 tablespoon of the parsley. Return the heat to medium-high and simmer 2 minutes, or until the sauce slightly thickens.
Finish the sauce by whisking in the remaining tablespoon of butter. Once it's completely incorporated, kill the heat and immediately spoon sauce over fish.
Garnish with the remaining parsley and serve.