For anchovy mayonnaise, process egg yolks, mustard and verjuice in a food processor until well combined. With motor running, gradually add olive oil in a steady stream until mixture is thick, add anchovies and process until combined. Season to taste with sea salt and freshly ground black pepper. Mayonnaise will keep refrigerated for up to 2 weeks.
Rinse vegetables under cold running water to remove any dirt. Arrange vegetables on a large platter and serve with anchovy mayonnaise.