Place the salmon in a large baking dish. Combine butter, 4 tablespoons lemon juice, and lemon zest and pour the mixture over the salmon. Season with salt and pepper and marinate for 1 to 2 hours.

Preheat an outdoor grill to medium-high heat.

Meanwhile, mix the cream cheese, tarragon, and 1 teaspoon lemon juice together and set aside. In another bowl, blend together eggs, heavy cream, hot pepper sauce, and salt and pepper, to taste, and set aside.

Preheat a nonstick skillet for the eggs by placing the pan on the grill. At the same time, place the salmon on the grill and cook until desired doneness, about 5 minutes per side.

Pour egg mixture into the pan and cook the eggs by continually moving cooked portions toward the center of the pan allowing the uncooked portion to flow to the sides, flipping when close to set.

Place bagels on the grill cut side down and toast. Remove and spread a portion of the cream cheese mixture on the toasted side of each bagel. Place the bagels on serving plates. Top with cooked egg, salmon, and hollandaise sauce. Garnish with chopped chives and parsley.