Preheat your oven to 425°F (220°C). Line a large baking sheet with parchment paper for easy cleanup.
In a medium mixing bowl, combine the diced potatoes with olive oil, salt, and black pepper. Spread them evenly on one side of the baking sheet.
Roast the potatoes in the preheated oven for about 20 minutes, or until they begin to turn golden and are crispy on the edges, stirring halfway through.
While the potatoes cook, prepare the broccoli. Toss the broccoli florets with a drizzle of olive oil, salt, and pepper. After the potatoes have roasted for 20 minutes, add the broccoli to the baking sheet and return to the oven. Roast for an additional 15-20 minutes until the broccoli is tender and slightly caramelized.
While the vegetables are roasting, melt the butter in a small saucepan over medium heat. Add the minced garlic and sauté for 1-2 minutes until fragrant. Remove from heat and stir in the juice and zest of one lemon.
Season the salmon fillets with salt and black pepper. In the last 10 minutes of roasting, push the vegetables to the sides of the baking sheet and place the salmon fillets in the center. Drizzle the lemon butter sauce over the salmon and place lemon slices on top.
Return the baking sheet to the oven and bake until the salmon is cooked through and flakes easily with a fork, about 10-12 minutes.
Serve the salmon alongside crispy potatoes and roasted broccoli. Drizzle any remaining lemon butter over the top and garnish with fresh parsley if desired.