In a blender or food processor, combine oil, anchovies, and garlic. Cover and blend or process just until anchovies and garlic are finely chopped.
Pour anchovy mixture into a small saucepan. Add butter. Cook over medium-low heat until mixture is bubbly, stirring occasionally.
If desired, keep warm in a 1-1/2-quart slow cooker on low-heat setting for up to 2 hours. Serve dip with vegetables. Makes 1-1/2 cups.
To blanch vegetables, cook desired vegetables in boiling, lightly salted water for 2 minutes; drain. Immediately plunge vegetables into a bowl of ice water; cool. Drain well.