Place eggs in the bottom of a small pot. Cover with cold water and heat until boiling. Remove from heat and let stand, covered for 9 minutes. Immediately transfer to an ice bath. Drain and peel eggs. Set aside.
In a skillet, cook bacon over medium heat until crisp. Place on a paper towel-lined plate to drain.
Slice each egg in half lengthwise and gently remove yolks to a bowl. Add mayonnaise, capers, dill, chives and grainy mustard to yolks. Mash together until well combined. Stuff mix into egg whites, dividing equally.
Arrange a cooked bacon slice, breaking pieces to fit as necessary, on 12 stuffed egg halves. Top with a small piece of lettuce and a slice of tomato. Finish with securing remaining egg halves on top of sliders with a cocktail pick.
Sprinkle with dill and everything bagel seasoning just before serving.
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