Preheat your oven to 425°F and line two large sheet pans with parchment paper. This prep step ensures nothing sticks and guarantees even browning across all ingredients.
Toss baby potatoes with 1 tablespoon olive oil, half the salt, and pepper on the first sheet pan. Spread them in a single layer and roast for 10 minutes before adding other vegetables. This head start ensures potatoes cook completely in your 30 minute timeframe.
Meanwhile, place salmon fillets skin-side down on the second sheet pan and brush with remaining olive oil. Sprinkle garlic powder, paprika, remaining salt, and black pepper evenly across each fillet's surface.
After potatoes have roasted for 10 minutes, remove the first pan and scatter broccoli florets and asparagus spears around the potatoes. Drizzle vegetables with melted butter mixed with minced garlic and fresh dill. Return to oven immediately.
Place your 30 minute salmon dinner family summer recipe in the oven on the second rack. Bake both sheet pans for exactly 12 minutes, until salmon flakes easily with a fork and vegetables are tender-crisp with caramelized edges.
While everything roasts, whisk together Dijon mustard, remaining butter, fresh dill, and lemon juice in a small bowl. This creates a bright sauce that elevates the entire plate when drizzled over salmon and vegetables.
Remove both pans from the oven and immediately squeeze fresh lemon over salmon fillets and vegetables. Drizzle the mustard-dill sauce across each plate just before serving for maximum flavor impact.