Add the eggs, garlic, mustard, salt, pepper, and anchovy fillet to a food processor and puree. Add the lemon juice and puree to combine. With the machine still running, add the oils in a slow, steady stream and process until the mixture has formed a thick emulsion. Add the parsley and pulse to combine. Transfer the aļoli to a small nonreactive bowl and stir in the capers. Refrigerate until ready to use, up to 1 week.
Yield: Generous 2 cups