Combine the egg yolk, mustard, garlic, anchovies, lemon juice, salt and pepper into the bowl of an electric food processor. Process until smooth, scraping down the sides of the bowl with a rubber spatula as needed. With the food processor running, very slowly pour the olive oil, and then the vegetable oil through the feed tube, adding only a few drops at a time and allowing the oil to incorporate fully and thicken the sauce. Add the grated Parmesan and pulse a few times to combine. This can be kept refrigerated in an air-tight container for about 2-3 days.