Preheat your oven to 400°F (200°C). Line a baking sheet with parchment paper.
In a large bowl, toss the halved baby potatoes with 1 tablespoon of olive oil, salt, and pepper. Spread them out on one side of the prepared baking sheet.
Roast the potatoes in the preheated oven for 20 minutes.
While the potatoes are roasting, prepare the lemon butter sauce. In a small saucepan over medium heat, melt 2 tablespoons of butter. Add minced garlic, lemon zest, lemon juice, and dried thyme. Stir and cook for about 2 minutes until fragrant. Remove from heat.
After 20 minutes, remove the baking sheet from the oven. Push the potatoes to one side and place the salmon fillets on the other side. Drizzle the lemon butter sauce over the salmon. Season with salt and pepper.
Add the broccoli florets to the baking sheet, tossing them with a little olive oil, salt, and pepper.
Return the baking sheet to the oven and roast everything for an additional 15 minutes, or until the salmon is cooked through and flakes easily with a fork.
Remove from the oven, garnish with chopped parsley, and serve immediately.