Pat the cod fillets dry with paper towels and season both sides with salt and pepper.
Place the flour in a shallow dish. Dredge each fillet in the flour, shaking off any excess.
In a large skillet, heat the olive oil and 2 tablespoons of butter over medium-high heat until the butter is melted and bubbly.
Add the cod fillets to the skillet, cooking for about 3-4 minutes on each side, or until golden brown and cooked through. The fish should flake easily with a fork.
In the last minute of cooking, add the remaining 2 tablespoons of butter and lemon juice to the skillet, spooning the melted butter over the fillets.
Remove the cod from the skillet and transfer to a serving platter. Drizzle with any remaining butter sauce from the skillet and garnish with fresh parsley.
Serve immediately with lemon wedges on the side.