Stir together the panko, dill, lemon zest and 1 tablespoon of the melted butter in a medium bowl; set aside.
Butter the bottom of a 2-quart casserole dish. Layer half the potatoes, overlapping, to cover the bottom of the dish. Sprinkle with half of the feta and 1/2 teaspoon each salt and pepper. Repeat, topping with the remaining potatoes, feta and 1/2 teaspoon each salt and pepper. Combine the broth and 1 tablespoon of the melted butter in a small bowl and pour over the potatoes. Cover with foil and bake until the potatoes are just softened, 40 to 45 minutes.
Meanwhile, cut the salmon into 2- to 3-inch pieces. Toss the salmon with the lemon juice and remaining 1/4 teaspoon salt.
Remove the potatoes from the oven and uncover. Increase the oven to 425 degrees F. Place the salmon on the potatoes and sprinkle with the panko mixture. Bake, uncovered, until the salmon is cooked through and the panko is golden brown, 12 to 15 minutes. Garnish with dill sprigs.