Preheat the oven to 425°F (220°C). High, dry heat encourages Maillard browning on the sweet potatoes and edges of the salmon while roasting the broccoli quickly so it stays bright and not mushy.

Season the sweet potatoes: in a large bowl toss the 1" sweet potato cubes with 1 tablespoon olive oil, 3/4 tsp kosher salt, 1/2 tsp black pepper and 1/2 tsp smoked paprika. Toss until evenly coated. Coating the cubes in oil and seasoning helps the exterior caramelize and the paprika will toast in the oven, adding a smoky note.

Spread the sweet potatoes in a single layer on a rimmed baking sheet (use parchment for easier cleanup). Give each cube space — overcrowding steams instead of roasts, preventing crisp edges. Place the pan on the middle rack and roast for 15 minutes.

While the potatoes start roasting, prepare the salmon and broccoli. Pat the salmon fillets dry with paper towels (this helps the surface brown). In a small bowl combine the minced garlic, lemon zest, remaining 1 tablespoon olive oil, 1/4 tsp smoked paprika, 1/2 tsp dried thyme (or rosemary), and a pinch of salt and pepper. Brush or rub this mixture over the flesh side of each fillet — the oil carries the aromatics into the fish and the zest adds bright citrus perfume.

Toss the broccoli florets in the bowl used for the salmon (no need for extra bowls): add 1/4 tsp kosher salt, 1/4 tsp black pepper and a light drizzle of olive oil if needed. The small amount of seasoning will promote browning and help the florets crisp without burning.

After the sweet potatoes have roasted 15 minutes, remove the pan from the oven. Push the potatoes to one side and arrange the broccoli in a single layer on the empty space. Place the salmon fillets skin-side down on the pan with a little space between them. Positioning everything on one pan lets the vegetables caramelize while the salmon roasts quickly; placing salmon skin-side down protects the flesh from direct heat and helps release the fillet after cooking.

Return the pan to the oven and roast for 10–12 minutes. Salmon doneness: check at 10 minutes — a 6 oz fillet is usually medium-rare at 10–11 minutes (internal temp 125–130°F / 52–54°C); cook to 145°F (63°C) if you prefer well done. The broccoli should be tender with charred tips and the sweet potatoes golden at the edges. Baking everything together for the last stage concentrates flavors and saves time.

Finish and rest: remove the pan and immediately squeeze the lemon juice over the salmon and vegetables. Rest the salmon 2–3 minutes — resting lets the juices redistribute and prevents them from cascading out when you slice, keeping the fillet moist.

Serve: plate each fillet with an even portion of roasted sweet potatoes and broccoli. Spoon any pan juices over the salmon for extra flavor and a touch more moisture. Optionally finish with a light drizzle of good olive oil and an extra pinch of flaky salt for contrast.