Preheat the oven to 400ºF. In a small bowl, combine the butter, olive oil, garlic, paprika, salt, and chopped parsley. Stir until it forms a fairly smooth paste.
Add the cod filets to a baking dish, add the garlic butter mixture on top of the fish, the spread it until the fish is evenly coated.
Cut half of the lemon into slices and add the lemon slices on top of the fish. Cut the remaining ½ lemon into wedges for serving.
Bake the cod for 15-20 minutes, or until it flakes easily with a fork and the internal temperature reaches 145ºF (total baking time will depend on the thickness of the filets and the material of your baking dish). Spoon any juices from the bottom of the pan over the fish. Serve the cod immediately with the remaining fresh lemon wedges for squeezing juice over top.