Remove the salmon from the refrigerator 15 to 20 minutes before cooking to bring it closer to room temperature.
Pat the salmon fillets completely dry on all sides using paper towels. Generously season the flesh and skin with kosher salt and black pepper.
Heat the olive oil in a large skillet over medium-high heat until shimmering and hot.
Carefully place the salmon fillets skin-side down in the pan. Gently press down on each fillet with a spatula for 10 seconds to ensure the skin makes full contact with the pan.
Cook undisturbed for 4 to 5 minutes, allowing the skin to become crispy. Watch the side of the fillet; the flesh will lighten from the bottom up. Once it is opaque about 3/4 of the way up, flip the salmon.
Cook on the flesh side for an additional 1 to 2 minutes until cooked to your desired doneness, then transfer the salmon to a plate.
Reduce the skillet heat to low. Add the butter and minced garlic, cooking for about 1 minute until fragrant.
Stir in the lemon juice and fresh dill. Spoon the pan sauce over the resting salmon fillets and serve immediately.