Boil potatoes in salted water for 18 minutes until fork tender, then drain thoroughly.
Mash potatoes with 4 tablespoons butter, warm milk, and salt until completely smooth and creamy.
Pat salmon fillets dry with paper towels and season flesh with salt and pepper.
Heat olive oil in a skillet over medium-high heat and sear salmon skin-side down for 5 minutes.
Flip fillets and cook 3 minutes longer until cooked through, then transfer to a warm platter.
Melt remaining butter in skillet with garlic for 1 minute, spooning over salmon and potatoes.
