1. Melt butter in a small saute pan over medium-low heat. Add garlic, and cook until softened but not browned, 1 to 2 minutes. Add anchovies and oil, and reduce heat to low. Cook, stirring occasionally, until mixture is softened and lightly browned, about 20 minutes. Remove from heat; let cool slightly.

2. Transfer the mixture to the jar of a blender, and add milk; puree until thick and smooth, about 2 minutes. Transfer to an airtight container, and store in the refrigerator until ready to serve, preferably overnight and up to 4 days.