In a small saucepan, combine the clam juice, dry sherry, whole milk, minced shallots, minced garlic, and bay leaf. Set over medium-high heat and bring to a gentle simmer. Allow the liquid to reduce by half, concentrating its flavors into a rich and aromatic base.

In a separate saucepan (at least 1-quart capacity), melt one tablespoon of unsalted butter over medium heat until it becomes foamy. Sprinkle in the flour while continuously whisking to create a smooth, lump-free mixture. Stir for a couple of minutes until the roux takes on a light tan color, ensuring it does not brown.

Gradually pour the reduced liquid into the roux, whisking vigorously to combine. Expect the mixture to bubble up initially—continue whisking steadily to achieve a smooth consistency as the sauce thickens.

Lower the heat to its lowest setting and remove the bay leaf. Begin adding the unsalted butter, two tablespoons at a time, whisking continuously to ensure each portion fully melts and emulsifies into the sauce before adding the next.

Once all the butter is incorporated, stir in the lemon juice, salt, and white pepper. If the sauce appears too thick, adjust the consistency by adding a small amount of clam juice or water. Serve warm, draped over seafood, vegetables, or poultry for a luxurious finishing touch.