Combine garlic and milk in a 1- to 1 1/2-quart heavy saucepan and gently simmer over low heat, uncovered, until garlic is very tender, about 20 minutes. Cool slightly, about 5 minutes, then purée mixture with anchovies, oil, and mayonnaise in a blender until smooth. (Use caution when blending hot liquids.) Add more milk to thin if necessary.