Cook six eggs in boiling water over medium-high heat for 10 to 12 minutes. Let cool completely, then peel.
Halve the eggs lengthwise with one clean cut of a thin, sharp knife. Scoop the yolks into a bowl with a small coffee spoon.
Add the sour cream, mayonnaise, Chick-fil-A sauce, Dijon mustard, vinegar, and salt to the yolks. Mash with a fork, then rub against the side of the bowl with a spatula until smooth and creamy.
Scoop the filling generously with a round tablespoon measuring spoon, then use a small coffee spoon to slide it onto each egg white in a rounded mound.
Top with a dot of whole-grain mustard or a topping of your choice.