This versatile condiment can be made up to a day in advance and refrigerated until serving.
Combine lemon juice, vinegar, garlic, paprika, egg, and egg yolk in the bowl of a food processor. Process just until ingredients are blended.
With processor running, slowly drizzle vegetable oil into mixture (it should begin to come together like mayonnaise). Add tarragon; season with salt and pepper. Slowly drizzle olive oil into processor. Chill for 30 minutes, and serve.
Raw eggs should not be used in food prepared for pregnant women, babies, young children, the elderly, or anyone whose health is compromised.