Step 1

Adjust oven rack to middle position and heat oven to 325 degrees. Dissolve 5 tablespoons salt in 2 quarts water in large container. Submerge salmon in brine and let stand at room temperature for 15 minutes. Remove salmon from brine, pat dry, and set aside.

Step 2

Meanwhile, melt butter in 10-inch skillet over medium heat. Add panko and 1/8 teaspoon salt and season with pepper; cook, stirring frequently, until panko is golden brown, 4 to 5 minutes. Transfer to bowl and let cool completely. Stir in egg and thyme until thoroughly combined. Stir tarragon, mustard, and mayonnaise together in second bowl.

Step 3

Set wire rack in rimmed baking sheet. Place 12 by 8-inch piece of aluminum foil on wire rack and lightly coat with vegetable oil spray. Evenly space fillets, skin side down, on foil. Using spoon, spread tarragon mixture evenly over top of each fillet. Sprinkle panko mixture evenly over top of each fillet, pressing with your fingers to adhere. Bake until center of thickest part of fillets reaches 125 degrees and is still translucent when cut into with paring knife, 18 to 25 minutes. Transfer salmon to serving platter and let rest for 5 minutes before serving with lemon wedges.