Preheat oven to 400°F (200°C) and prepare a baking sheet with parchment paper or grease.
Toss halved baby potatoes with 2 tablespoons olive oil, salt, and pepper; spread evenly on the baking sheet.
Roast potatoes for 15 minutes, then add broccoli florets to the sheet, drizzle with remaining 1 tablespoon olive oil, and toss gently.
Continue roasting potatoes and broccoli together for another 15 minutes until golden and crispy.
Season salmon fillets with salt and pepper.
Heat 2 tablespoons butter in a large skillet over medium heat, then sear salmon skin-side down for 3-4 minutes per side until cooked through and golden.
Remove salmon from skillet and set aside.
In the same skillet, sauté minced garlic over medium heat for 30 seconds to 1 minute until fragrant.
Pour in broth, scraping up browned bits with a wooden spoon.
Stir in heavy cream, lemon juice, lemon zest, and Dijon mustard; simmer for 3-4 minutes until sauce thickens slightly.
Add chopped parsley and stir to combine.
Return salmon fillets to the skillet, spoon sauce over them, and cook for 2 more minutes to warm.
Serve salmon on a bed of roasted potatoes and broccoli, drizzled with lemon butter sauce and garnished with extra parsley if desired.