Combine lemon juice, garlic, mustard, anchovies(and the oil they came in!) and pepper in a blender. Cover blender and pulse blender to roughly combine all ingredients. When combined, blend on low until smooth (aprox 20 seconds.) Scrape down sides of blender to make sure everything is incorporated. Taste and adjust to your preference with a bit more lemon juice, mustard, salt or pepper. Once satisfied with flavor proceed to next step.
With blender running on low speed setting, drizzle olive oil in until dressing is extended and well combined (aprox 30 seconds.) Use immediately or refrigerate in a sealed container to have on hand.