Preheat and prep: Preheat your oven to 425°F (220°C). Line a large rimmed baking sheet with parchment or a light layer of oil. Preheating ensures the sweet potatoes hit a hot surface for instant caramelization (browning), which builds flavor and texture.

Prepare the sweet potatoes: Peel if you prefer (skin is fine and adds texture), then cut into 1/2-inch (12 mm) cubes — aim for uniform pieces so they roast evenly. Place the cubes in a bowl and toss with 1 tbsp olive oil, 1/2 tsp kosher salt and a pinch of black pepper. The oil promotes Maillard browning; salt draws moisture to the surface to help create crisp, browned edges.

Roast the sweet potatoes: Spread the cubes in a single layer on one side of the prepared baking sheet (don’t overcrowd). Roast for 20 minutes, then stir/turn and roast another 7–12 minutes until edges are deeply golden and interiors are tender when pierced. If the pan is too crowded they’ll steam instead of roast; spacing = caramelization.

Prep the green beans: While the potatoes begin roasting, trim the green beans and pat them dry. In a bowl toss the beans with the remaining 1 tbsp olive oil, the minced garlic, 1/4 tsp kosher salt and 1/4 tsp pepper. Dry beans will blister and caramelize; garlic added now will flavor the oil and the beans but won’t burn if you roast at 425°F for a short time.

Toast the almonds: Heat a small dry skillet over medium heat and toast the sliced almonds 2–3 minutes, stirring, until fragrant and just golden — watch closely because nuts can go from toasted to burnt very fast. Transfer to a small bowl; they’ll continue to crisp slightly off heat. Toasting releases volatile oils and deepens the nutty flavor.

Add beans to the oven: After the sweet potatoes have roasted 20 minutes, push them to one side of the sheet and add the green beans in an even layer on the other side. Roast both together another 10–12 minutes until the beans are bright, blistered in spots and crisp-tender. This staggers cook times so everything finishes simultaneously.

Prep the salmon while vegetables finish: Pat salmon fillets thoroughly dry with paper towels — moisture prevents a good sear. Season both sides with the remaining 1/4 tsp kosher salt and a pinch of black pepper. If the fillets are uneven, press the tail to more even thickness with your fingers (or use kitchen twine) so they cook evenly.

Sear the salmon: Heat a heavy oven-safe skillet (cast-iron preferred) over medium-high heat until shimmering. Add the additional 1 tbsp olive oil and swirl. Place salmon skin-side down and press gently for 10–15 seconds to ensure the skin makes full contact — this creates an evenly crisp skin. Sear skin-side down for 3–4 minutes without moving; you want a deep golden crust (Maillard reaction) which adds flavor and helps the fillet hold together.

Finish in the oven: After searing, transfer the skillet to the hot oven (or transfer the fillets to a baking dish skin-side up) and roast 5–7 minutes for medium (internal temp 125–130°F / 52–54°C) depending on thickness. The oven’s dry heat cooks the fish gently through without over-charring the crust. Rest 3 minutes after cooking — carryover will bring the temperature up a few degrees and juices will redistribute.

Make the lemon-herb dressing: While the fish rests, whisk together the lemon zest and 1–2 tbsp fresh lemon juice, the chopped parsley or dill, the toasted almonds (reserve a small pinch to finish the plates), and a drizzle (about 1 tsp) of the pan juices or 1 tsp olive oil if the pan is dry. Add a small pinch of salt and pepper to taste. The acid brightens the fatty salmon and the herbs add fresh aromatics; a little pan jus carries savory brown flavors into the dressing.

Finish the green beans and assemble: Toss the roasted green beans with most of the toasted almonds and a grind of fresh black pepper. Portion the sweet potatoes and green beans onto two plates. Place a salmon fillet on each plate, spoon the lemon-herb dressing over the top (and a little around the plate), then finish with the reserved almonds and an extra sprinkle of fresh herbs and a lemon wedge. Contrast in texture (crispy skin, tender flesh, crunchy almonds, and creamy sweet potato) makes this dish sing.

Serve and enjoy: Serve immediately while the salmon is warm and the vegetables still have some snap. Encourage squeezing extra lemon over the fish for those who want a brighter finish.