Combine oil and butter in a small saucepan, and place pan over medium-low heat. Cook until butter has melted and is foamy, about 8 minutes. Reduce heat to low.
Add garlic, and simmer 1 minute more, being careful garlic doesn't brown.
Add anchovies, and whisk until they have melted, about 5 minutes. Remove pan from heat. Transfer sauce to a bowl; serve.