Heat butter in an 8" skillet over medium heat; cook, stirring, until solids turn dark brown, 20-25 minutes. Remove from heat; whisk in vinegar and lemon juice, season with salt and pepper; set sauce aside.
STEP 2: In a shallow dish, whisk together milk and eggs; put flour into another shallow dish. Season fish with salt and pepper.
STEP 3: Working with one filet at a time, dip fish in flour, shake off excess, and then dip in egg mixture and shake off excess. Return filets to flour; transfer to a rack over a baking sheet.
STEP 4: Put the clarified butter in a non-stick sauce pan and heat over medium high heat.
STEP 5: When melted, place the fish skin side down in the sauce pan and cook each side for 3 minutes, until you see coloration, then drain on paper towels.
STEP 6: To serve, divide fish between 4 plates; sprinkle almonds on top. Whisk sauce and spoon over fish. Garnish with parsley; serve with lemon slices.