Make mayonnaise by combining the first 7 ingredients in a small bowl. Cover and refrigerate until needed.
Preheat your grill to medium-high. Grill sausages 6 to 8 minutes, turning occasionally, or until cooked through. If serving as an appetizer, slice the sausages into 1- to 2-inch pieces, set on a platter and serve with a bowl of the mayonnaise for dipping. If serving as a main-course, set 2 sausages on each of three plates. Place a dollop or two of the mayonnaise on each plate and serve.
Note: Keep any leftover mayonnaise refrigerated in a tight-sealing jar. It will keep about a week.