Combine the milk, parsley stalks, bay leaf, onion, mace, and peppercorns in a small pan.
Bring the mixture slowly to a simmer, then pour into a bowl and cool completely.
Strain the cold milk back into the pan and discard the aromatic flavourings.
Add the flour and butter to the pan and bring to a simmer while whisking continuously until smooth.
Reduce heat to the lowest setting and cook gently for several minutes, stirring occasionally.
Stir in the chopped parsley, cream, and lemon juice.
Season to taste and serve immediately in a warm jug.