Pat the fillets dry on both sides with paper towels and check for pin bones with a fingertip, pulling any out with tweezers. Season with 1/2 tsp salt and the pepper. Spread the flour on a plate, dredge each fillet on both sides, and shake off the excess until only a thin dusting remains.
Set a 20 cm / 8-inch skillet over medium heat and add the almonds dry. Stir constantly for 3 to 4 minutes until light gold and nutty-smelling, then tip them onto a plate right away because they keep darkening in the hot pan. Keep the skillet for the sauce.
Heat a 30 cm / 12-inch skillet over medium-high for 2 minutes and add 1 tbsp of the olive oil. When it shimmers, lay 2 fillets skin-side down, pressing each flat with a fish spatula for 10 seconds. Cook 3 to 4 minutes until the skin is crisp and golden and the flesh looks opaque about two-thirds of the way up the side.
Flip the fillets and cook about 1 minute, until the thickest part reads 145 F / 63 C and the flesh flakes. Move them to a warm plate skin-side up and tent loosely with foil. Carefully wipe out the pan, add the remaining 1 tbsp oil, and cook the other 2 fillets the same way.
Return the small skillet to medium heat and melt the butter with the garlic for 1 to 2 minutes, until the foam settles and the butter smells nutty with pale gold flecks. Take the pan off the heat, discard the garlic, and stir in the lemon juice (it will spit), parsley, pinch of salt, and toasted almonds.
Plate the fillets skin-side up and spoon the almond butter along one side so the skin stays crisp. Serve right away with the lemon wedges.