1. Allow eggs to come to room temperature, then separate 1/2 of the eggs and set the white aside for another use.
2. In your food processor with s-blade attached, blend the whole egg and egg yolk, mustard, salt, garlic, and lemon juice until well combined.
3. Using the drizzle feature or pouring very slowing, add the olive and avocado oils drop by drop.
4. You are essentially making mayonnaise, and it will begin to emulsify into a thick sauce. If it doesn’t, don’t worry. It will still taste great.
5. When desired consistency is reached, add capers with a splash of brine and blend until smooth. Season with ground pepper to taste.
6. If storing for later in the fridge, note that the dressing will harden when cold. Allow 15-20 minutes at room temperature to soften before serving.