Slice each egg in half lengthwise and remove the yolk. Put all the yolks in a small mixing bowl and all the whites on a platter.
Add vinegar, mayo, mustard, and salt to the yolks and mix with a fork until well combined and fluffy.
Fold in half of the crumbled bacon, tomatoes, and basil (reserving a little of the basil for a garnish).
Spoon fill the mixture into the centers of the whites. Garnish with remaining basil, tomatoes, bacon, and a sprinkle of the Smokey Bacon Sea Salt.