Preheat the oven to 275 degrees Fahrenheit. To make cleaning easier, line a rimmed baking sheet with parchment paper. Remove the salmon from the fridge to remove some of the cold.
Combine the sour cream, 2 tablespoons mustard, dill, capers, caper brine, salt, and pepper in a small mixing basin. Zest half of the lemon into the bowl, then split it in half and squeeze in half of the juice. To blend, mix everything together. If the sauce is too thick, add a little splash of water at a time until it thins out (or add extra lemon juice if desired).
Place the salmon, skin side down, on a baking sheet lined with parchment paper. Using a paper towel, pat it dry. Spread a heaping dollop (approximately 3 tablespoons) of the mustard sauce over the salmon in a thin layer.
Roast the salmon for 35 to 50 minutes, depending on the form of your salmon, until it is just barely cooked through, still wonderfully juicy, and flakes easily with a fork when removed (135oF when tested with an instant read thermometer).
Allow the salmon to rest for 5 minutes, during which time it will rise 5oF.
Drizzle the leftover sauce over the salmon, or serve it on the side, and garnish with fresh dill sprigs.