Preheat the broiler.
Melt the butter in a saucepan over moderate heat. When the foam subsides, remove the pan from heat and add the flour. Return to low heat and cook, stirring constantly, for two minutes. Do not let the "roux" brown.
Remove the pan from the heat again and slowly pour in the reduced poaching liquid from the scallops and the milk, whisking constantly. Return the pan to high heat and cook, stirring constantly with a whisk. When the sauce thickens and comes to a boil, reduce the heat and simmer slowly for 10 minutes.
Mix the egg yolks and 1/2 cup cream together in a bowl, then stir into it 2 tablespoons of the hot sauce from above. Add 2 more tablespoons and whisk this mixture back into the simmering sauce.
Over moderate heat, bring the sauce to a boil, stirring constantly, and simmer for 30 seconds. Remove from heat and season with lemon juice, salt and pepper. The mixture should coat a spoon fairly thickly. If the sauce is too thick and pasty, add some more cream. Adjust the seasoning.