Pour enough water into a large baking dish to fill about halfway. Stir 1/2 cup salt into water until dissolved; add tarragon. Place salmon in the brine, adding more water if needed to completely cover salmon. Cover dish with plastic wrap and refrigerate until brine has soaked into the salmon, 2 to 12 hours.
Whisk mayonnaise, lemon juice, garlic, pepper, lemon zest, and 1 pinch salt together in a bowl until aioli is smooth; refrigerate until chilled, about 30 minutes.
Remove salmon from brine and place on a wire rack to dry, about 30 minutes. Discard brine.
Place apple wood chips in the smoker. Place salmon in the smoker and smoke according to the manufacturer's instructions on low heat until salmon flakes easily with a fork, 1 1/2 to 2 hours.
Assemble sliders by dividing the salmon among the 12 buns. Top each piece of salmon with a spoonful of aioli. Place top bun on aioli layer creating a sandwich.