Heat the butter in a saucepan until melted. Add the onion and cook 4-5 minutes, until softened.

Sprinkle the flour in and stir until incorporated, then cook a few minutes, stirring.

Add the broth and milk slowly, stirring to mix in each addition so the mixture doesn't get lumpy.

Bring to a simmer and cook a few minutes, until thickened.

Taste and add the salt and pepper, then add the chicken and parsley.

Heat through and serve over toast, noodles, rice, or whatever suits your fancy.