Preheat your oven to 425°F (220°C) and line a large sheet pan with parchment paper or lightly oil it.
In a bowl, toss the cubed sweet potatoes with 1.5 tablespoons of olive oil, half of the minced garlic, paprika, oregano, salt, and pepper. Spread them out in a single layer on the sheet pan.
Roast the potatoes for 12 minutes to start caramelizing the edges.
Meanwhile, in a small bowl, whisk together the melted butter, remaining garlic, lemon juice, a pinch of salt, and pepper.
Push the potatoes toward the edges of the pan to make space for the salmon. Place the salmon fillets on the center of the pan and brush them with half of the garlic butter mixture. Drizzle the salmon with a teaspoon of olive oil.
Toss the sweet potatoes once or twice during roasting, then spoon the remaining garlic butter over the salmon. Return the pan to the oven and bake for another 8-12 minutes, depending on the thickness of the fillets, until the salmon is opaque and flakes easily and the potatoes are tender.
Remove from the oven, spoon any pan juices over the salmon, and finish with chopped parsley if desired. Serve warm.