Preheat your oven to 425°F and line a baking sheet with heavy-duty aluminum foil, if desired, for easier cleanup. Spray the foil with cooking spray to prevent sticking.
Place the halved or quartered baby Yukon Gold potatoes in a large bowl. Drizzle with 3 to 4 tablespoons of olive oil and season generously with kosher salt and freshly ground black pepper. Toss the potatoes with your hands until they are evenly coated.
Spread the seasoned potatoes evenly on the prepared baking sheet and bake for about 15 minutes, or until they are about 75% done. You want them to be just tender but not fully cooked.
While the potatoes are baking, take a small microwave-safe bowl and add the unsalted butter. Heat on high power for about 45 seconds or until melted. Then, stir in the lemon juice and Dijon mustard until well combined. Set this flavorful mixture aside.
After 15 minutes, remove the baking sheet from the oven. Flip the potatoes to ensure even cooking and place the salmon fillets skin-side down on the baking sheet among the potatoes.
Drizzle the salmon with the remaining 2 to 3 tablespoons of olive oil and nestle the potatoes around the salmon fillets.
Pour about two-thirds of the lemon butter Dijon mixture over the salmon fillets, allowing some of it to drizzle onto the potatoes as well. This will help to flavor everything beautifully.
Evenly season the salmon with additional kosher salt and black pepper to taste.
Bake for an additional 10 minutes, or until the salmon is cooked through and flakes easily with a fork, and the potatoes are fork-tender.
If you desire a crispier finish, place the baking sheet under the broiler for 2 to 3 minutes, but keep a close watch to prevent burning. Your goal is to achieve a lovely golden-brown color.
Optionally garnish with finely minced parsley before serving. Enjoy immediately for the best flavor!