Preheat and prep: Heat your oven to 425°F (220°C). High oven heat creates fast caramelization on the sweet potato cubes so they brown without drying out. Line a rimmed baking sheet with foil or parchment for easy cleanup.

Cut and toss sweet potato: Place 1 medium sweet potato (about 150 g), peeled and cut into 1/2-inch (1–1.2 cm) cubes, in a bowl. Toss with 1 tablespoon olive oil, 1/4 tsp salt, and a few grinds of black pepper. Spread the cubes in a single layer on the prepared baking sheet; crowding prevents browning by steaming the pieces.

Roast the sweet potato: Roast on the top/middle rack for 20–22 minutes, turning once at 12 minutes. High heat and an initial space between pieces allow edges to caramelize; flipping ensures even browning. The cubes should be golden and tender when pierced with a fork.

Prep salmon and aromatics: While the sweet potato roasts, pat the 6 oz salmon fillet dry with paper towels — drying the surface is critical to getting a crisp sear. Season both sides with the remaining 1/2 tsp salt and 1/4 tsp pepper. Zest 1/2 lemon and reserve the zest; juice the lemon (about 1 tbsp). Mince 2 cloves garlic and finely chop 1 tsp fresh rosemary or thyme.

Heat the pan for the salmon: Place a heavy 10–12 inch skillet (preferably stainless steel or cast-iron) over medium-high heat and add 1 tablespoon olive oil. Let the oil heat until shimmering but not smoking — this ensures instant contact and Maillard reaction when the salmon hits the pan, creating a golden-brown crust.

Sear the salmon skin-side down: Gently place the salmon skin-side down in the hot pan and press lightly with a spatula for 10–15 seconds to ensure full skin contact (prevents curling). Cook undisturbed for 4–5 minutes — this gives the skin time to crisp and the heat to start cooking through from the outside in. You should see cooked color creeping up the side.

Finish the salmon: Flip the fillet and add 1 tsp butter, the minced garlic, and half the chopped herb (reserve the rest for finishing). Spoon the melted butter and aromatics over the top for 30–60 seconds as the fish finishes — this adds flavor and gloss without overcooking. Cook another 1.5–2.5 minutes depending on thickness; you want medium doneness (internal temp ~120–125°F for salmon when removed; it will rise to ~125–130°F while resting).

Rest the salmon: Transfer the salmon to a plate, tent loosely with foil and rest 3–4 minutes. Resting lets carryover heat finish cooking the interior while juices redistribute, keeping the fish moist.

Sauté the green beans: While the salmon rests (or in a second skillet earlier if you prefer multitasking), heat the remaining 1 tbsp olive oil over medium-high heat in a large sauté pan. Add the trimmed 2 cups (≈250 g) green beans and a pinch of salt. Sauté, stirring or shaking the pan, for 5–6 minutes until bright green and crisp-tender with a few charred spots — high heat cooks them quickly so they stay crisp rather than limp.

Finish the beans: Add the remaining chopped herb, a squeeze of lemon juice (1/2 tbsp), and a little lemon zest. Toss to combine and cook 20–30 seconds more to marry flavors. The acid brightens the beans and provides a counterpoint to the salmon’s richness.

Plate and serve: Spoon the roasted sweet potato onto your plate, arrange the green beans alongside, and set the salmon on top or next to them, skin-side up for crispness. Spoon any pan juices or garlic-herb butter over the fish and finish with a light sprinkle of flaky sea salt and the remaining lemon zest for brightness.

Taste and adjust: Taste a bean and a potato cube and adjust seasoning if needed. Serve immediately so the salmon skin stays crisp and vegetables remain vibrant and textured.