In a shallow bowl, whisk together flour, salt, black pepper, and cayenne pepper until evenly blended.

Pat perch dry with paper towels. Press each fillet into the seasoned flour, coating both sides. Shake off any excess.

Add oil and 2 tablespoons butter to a large skillet over medium-high heat. Swirl pan until butter foams and turns a light golden brown.

Carefully place fillets in the skillet, cooking 3–4 minutes per side until the crust is crisp and internal temperature reaches 145°F.

Reduce heat to medium, add remaining 2 tablespoons butter, and spoon the melted brown butter over fillets for an extra glossy finish.

Transfer perch to a platter, sprinkle with parsley, and serve immediately with lemon wedges.