Preheat the oven to 425°F (220°C). A hot oven gives the sweet potato edges a chance to caramelize and the salmon a quick roast so it stays moist inside while developing a lightly golden surface.

Toss the sweet potato cubes with 1 1/2 tbsp olive oil, 1/2 tsp garlic powder, 1 tsp chopped rosemary/thyme, 1 tsp kosher salt and 1/2 tsp black pepper. Spread in a single layer on a rimmed baking sheet lined with parchment or a silicone mat. Make sure the pieces are not crowded — crowded vegetables steam and won't brown.

Roast the sweet potatoes for 12 minutes, then shake the pan or flip pieces so they brown evenly. Starting them first gives them a head start because they take longer to become tender than broccoli and salmon.

While the sweet potatoes roast, pat salmon dry with paper towels (dry skin crisps more easily). Season the flesh side with 1 tsp garlic powder, 1 tsp chopped rosemary/thyme, 3/4 tsp kosher salt and 1/2 tsp black pepper. Drizzle the fillets with 1 tbsp olive oil and rub gently so the oil and seasonings adhere — oil helps conduct heat and encourages a glossy finish.

Cut the broccoli into uniform florets if needed. In a medium bowl, toss broccoli with the remaining 1/2 tbsp olive oil, a pinch of salt (about 1/4 tsp) and a grind of pepper. The light oil coating promotes even roasting and helps the florets brown rather than steam.

After the sweet potatoes have roasted 12 minutes, add the broccoli to the pan — arrange florets so they're cut-side down where possible for better browning. Return the pan to the oven and roast another 10 minutes. This staggers cooking so the vegetables finish at the same time and the broccoli becomes tender yet still bright green.

Make a lemon-butter (or lemon-olive oil) baste: in a small bowl, combine the lemon zest, lemon juice, and the optional 1 tbsp softened butter (or 1 tsp extra olive oil). The butter adds a glossy finish and mouthfeel; lemon brightens the dish and cuts through the salmon’s richness.

After the vegetables have roasted a total of ~22 minutes, push them to the sides of the sheet pan and place the salmon fillets skin-side down in the middle (or transfer vegetables to a second pan if you prefer more space). Spoon or brush half the lemon-butter mixture over the salmon. Roasting salmon on the same sheet pan for the final 10–12 minutes saves time and builds flavor from the roasted vegetables, but if you want maximum crust on the salmon, sear it skin-side down in a hot ovenproof skillet for 1–2 minutes first.

Roast everything for 10–12 minutes more at 425°F, depending on fillet thickness: an average 6-oz (170 g) fillet will be medium at about 10 minutes (internal temperature 125–130°F / 52–55°C). Cook a little longer for well-done (135°F+). Salmon continues to cook while resting, so remove it at the desired internal temp minus 3–5°F.

Remove the sheet pan from the oven. If you used butter in the lemon sauce, spoon the remaining mixture over the salmon and vegetables for shine and extra flavor. Let the salmon rest 2–3 minutes — this lets the juices redistribute so the flesh is silky, not dry.

Serve each fillet with a portion of roasted sweet potato and broccoli. Finish with another light squeeze of lemon and a small pinch of flaky sea salt if desired. The contrast of textures — crisped potato edges, tender broccoli, and buttery salmon — is the hallmark of this dish.