Allow this robust dip to mellow overnight in the refrigerator. Before serving, bring it to room temperature or reheat gently in a saucepan. Serve the dip in ceramic bowls set over warming candles with steamed broccoflower and toasted country bread.
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.
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.