In the bowl of a food processor, combine the egg, egg yolk, lemon juice, mustard, garlic, salt, and pepper. Process on high speed until smooth, light yellow, and frothy, about one minute. While the processor is still running, combine the vegetable and olive oils in a measuring cup with a pour spout, and working very slowly add the oil to the processor in a thin, steady stream, processing until the oil is completely incorporated and a thick emulsion is formed. (It is very important that the oil is added very slowly, especially at the beginning, otherwise the mayonnaise may break.) Transfer the mayonnaise to a nonreactive bowl, and add more salt, pepper, and/or lemon juice if desired. Use immediately, or refrigerate in an airtight, nonreactive container for up to 3 days.