Preheat oven to 425°F (220°C).
Place the quartered potatoes in a large pot and cover with cold water. Add a pinch of salt and bring to a boil over high heat. Reduce to medium and simmer until potatoes are tender, about 15 minutes.
While potatoes cook, toss asparagus with 1 tablespoon olive oil, 1/4 teaspoon salt, and 1/8 teaspoon black pepper. Spread on a baking sheet and roast in the preheated oven for 12-15 minutes until tender and slightly caramelized.
Pat salmon fillets dry with paper towels. Season both sides with 1/2 teaspoon salt and 1/4 teaspoon black pepper.
Heat 1 tablespoon olive oil in a large non-stick skillet over medium-high heat until shimmering.
Place salmon fillets skin-side down in the skillet. Cook without moving for 4-5 minutes until skin is crispy and golden brown.
Flip salmon fillets and cook for an additional 3-4 minutes until salmon is opaque and flakes easily with a fork. Remove salmon from skillet and set aside on a warm plate.
Reduce heat to medium-low. Add 1 tablespoon butter and minced garlic to the skillet. Cook for 1 minute until fragrant.
Add 1 tablespoon fresh lemon juice and 1 teaspoon chopped parsley to the skillet. Stir to combine and remove from heat.
Drain the cooked potatoes and return them to the pot. Add 2 tablespoons butter, 1/4 cup whole milk, and 1/4 teaspoon salt. Mash until smooth and creamy.
To serve, place a scoop of mashed potatoes on each plate, arrange roasted asparagus beside it, and top with a salmon fillet. Spoon the garlic lemon butter sauce over the salmon and garnish with a sprinkle of fresh parsley.