In a frying pan over medium heat, melt the butter.
Add the flour and cook, stirring, until it resembles wet sand and smells slightly nutty (about 1–2 minutes). This step cooks out the raw flour taste.
Slowly add the milk and cream, whisking continuously to prevent lumps. Make sure to whisk into the corners of the pan.
Continue whisking until the sauce thickens and becomes smooth.
Stir in salt, pepper, and lemon juice.
Add the fish fillets and reduce the heat to low. Spoon the sauce over the fish to ensure it is fully coated.
Cook gently until the fish is tender and flakes easily.
Gently stir in the parsley