Preheat the oven to 220°C (425°F). High, dry heat gives the sweet potatoes surface caramelization and helps the salmon develop a light crust without overcooking inside.

Prepare the sweet potatoes: cut the 800 g sweet potatoes into 1–1.5 cm (3/8–1/2 in) cubes so they roast evenly. Smaller pieces brown faster and become tender through in the same time as the salmon.

Toss the sweet potato cubes with 40 ml (about 2.5 tbsp) of the olive oil, 1 tsp kosher salt and 1/2 tsp freshly ground black pepper, and 2 smashed garlic cloves. Spread them in a single layer on a rimmed baking sheet lined with foil or parchment, leaving space in the pan for air circulation; crowding causes steaming instead of roasting.

Roast the sweet potatoes for 15 minutes on the top rack. This head start softens and begins caramelization so they finish at the same time as the fish without overcooking it.

While the potatoes roast, pat the 700 g salmon dry with paper towels — removing surface moisture promotes browning. If you prefer, leave the skin on; it crisps under high heat and helps hold the fillet together.

Season the salmon: lightly brush the fillets with 10 ml (2 tsp) olive oil, zest 1 lemon over them (zest adds aromatic oils for a citrus perfume), sprinkle 1/2 tsp kosher salt and 1/4 tsp black pepper, and tuck small rosemary or thyme leaves over the top if using.

After the potatoes have roasted 15 minutes, make room on the baking sheet and add the salmon fillets skin-side down. Scatter the remaining 2 garlic cloves (smashed) around the pan and return to the oven. Roasting the salmon with the potatoes lets the potato sugars deepen while the fish cooks gently from the surrounding heat.

Roast everything for another 10–12 minutes for medium doneness (internal temp ~52–54°C / 125–130°F) — salmon will continue to carryover cook while resting. If you like your salmon well-done, roast 14–16 minutes. Remove the baking sheet when the sweet potatoes are fork-tender and have golden edges.

While the salmon and potatoes finish, cook the green beans: bring a large pot of salted water to a rolling boil (salt flavors the beans and helps preserve their bright color). Blanch the 500 g trimmed green beans for 2–3 minutes until bright green and just tender; immediately plunge them into ice water to stop cooking and set color.

In a large skillet over medium heat, add the remaining 20 ml (about 4 tsp) olive oil. Add the minced 4 garlic cloves and sauté 20–30 seconds until fragrant but not browned — browning garlic turns it bitter. Add the drained green beans and toss to coat, seasoning with a pinch of salt and a squeeze of 1/2 lemon (about 1 tbsp). Toss 1–2 minutes just to heat through and marry the flavors; the quick pan finish keeps them crisp-tender.

Finish the salmon: when the fish comes out of the oven, top each fillet with a small pat (about 1 tbsp or 15 g) of butter to melt into the hot salmon for gloss and richness, then let rest 3 minutes. Resting allows juices to redistribute and keeps the fillet moist.

Plate: divide sweet potatoes, green beans, and salmon among 4 plates. Spoon any pan juices over the salmon, squeeze a lemon wedge over each portion, and finish with a light scattering of flaky salt or extra lemon zest if desired. Serve immediately.