Begin by boiling the diced potatoes in a large pot of water until tender—check for doneness by piercing with a knife; they should yield easily. Drain and set aside to cool slightly.
Meanwhile, heat a knob of butter in a skillet over medium heat. Add the salmon fillets and cook for about 3 minutes on each side, just until they begin to flake—don’t worry if they’re slightly underdone, as they’ll finish cooking in the oven. Remove the fillets from the pan, discard the skin, and gently break the fish into bite-sized flakes.
Using the same pan, reduce the heat and sauté the garlic and shallots for about one minute, just until softened and aromatic. Remove from heat and let cool slightly.
In a large mixing bowl, whisk together the eggs, crème fraîche or cream cheese, horseradish, and freshly chopped dill until smooth and well combined. Fold in the sautéed shallots and garlic, blending them into the creamy egg mixture.
Pour the egg filling into the prepared pie crust, spreading it out evenly. Arrange the flaked salmon and tender potatoes over the top, pressing them gently into the filling to ensure they’re nestled throughout the quiche.
Transfer the quiche to a preheated oven at 325°F (165°C) and bake for 20 to 25 minutes, or until the center is fully set and the top is lightly golden. Let cool slightly before slicing and serving.