Preheat oven to 450°F Season salmon with 1/4 teaspoon salt and 1/8 teaspoon pepper.
Melt 2 tablespoons butter in large nonstick skillet over medium heat. Add salmon and increase heat to medium high. Cook 1 to 1 1/2 minutes on one side until salmon just begins to brown lightly. Place salmon, browned side down, in small rimmed baking dish.
Melt remaining butter in same skillet over medium low heat. Add shallots and cook until fragrant, about 10 seconds. Spoon 1 tablespoon shallot mixture over salmon and sprinkle with 2 tablespoons dill or tarragon. Bake 4 to 7 minutes or until salmon just begins to flake.
Add snap peas to skillet and toss to coat with shallot mixture. Sprinkle with remaining dill or tarragon, salt and pepper. Cook peas until crisp-tender, about 2 to 3 minutes.
Divide peas between 4 dinner plates and top with salmon.