In a shallow dish, whisk flour, paprika, thyme, 1/2 teaspoon of the salt and 1/8 teaspoon of the cayenne. Place milk in another shallow dish. Set both aside.
In a large nonstick skillet, heat 1 tablespoon of the oil over medium-high heat. Dip fillets in the milk and shake off the excess. Dredge fillets in the flour and place in a single layer in the skillet.
Cook for about 5 to 6 minutes, turning halfway through cooking time or until golden brown. Repeat, using remaining oil as needed.
Remove to a plate lined with paper towels; keep warm.
Wipe out the skillet; melt butter over medium heat. Add walnuts, remaining cayenne and salt, and the black pepper. Cook, stirring frequently, until nuts are fragrant, about 2 to 3 minutes. Take off the heat. Stir in parsley and lemon juice.
To serve, spoon an equal amount of the nut mixture over each fillet. Serve with steamed snow peas and sautéed sweet peppers, if desired.