Put the eggs in a small saucepot. Add cold water to cover by about 1-inch. Bring the water to a boil over medium-low heat, then turn off the heat, cover and let sit for about 12 minutes.
Cool the eggs down in cold water, then peel and split lengthwise. Remove the yolks to a bowl and reserve the whites. Using a fork, mash the yolks with salt, pepper, to taste, and Dijon until smooth. Add the shallot, gherkins, brine and tarragon and stir to combine. If too thick, add a teaspoon more of gherkin brine liquid. Spoon into a resealable plastic bag and cut off a corner. Pipe the yolk mixture into the egg white halves. Top each half with a tarragon leaf. Arrange on a serving platter and serve.