You can also make a version of this recipe by stirring the basil, white pepper, and mustard into 1 cup of purchased mayonnaise. Add 2 to 3 tablespoons lemon juice to taste.
In a food processor or blender combine 1/4 cup of the basil, the salt, pepper, mustard, egg product, and lemon juice. Cover and process or blend until combined. Scrape down sides. Combine oils in a 1-cup glass measure. With the machine running, add oils in a thin, steady stream. Transfer mixture to a small bowl; stir in remaining basil. Makes 1-1/4 cups.