Serve right away, or cover and refrigerate.
Place 1/4 cup oil, garlic, and shallot in a skillet; turn on medium-low heat. When mixture sizzles, wait 30 seconds, then transfer to a food processor. Add remaining ingredients except salt and pepper; blend until smooth. Season with salt and pepper. Taste and add more lemon juice and/or honey, if desired. Drizzle with oil just before serving.