Set the oven to 450°F. Line a sheet pan with parchment paper. Spread the sweet potatoes into a single layer on the pan and toss with 1 to 2 tablespoons olive oil. Sprinkle with ½ teaspoon salt and a few grinds of black pepper. Toss gently to combine. Roast in the oven for 15 to 18 minutes.
While the potatoes are cooking, trim the broccolini into narrow stalks and rub the salmon with 1 tablespoon olive oil and salt and pepper to taste. Remove the sheet pan from the oven and place the broccolini and the salmon, skin-side-down, on the pan. Drizzle the broccolini with remaining olive oil and return to the oven to roast for another 8 to 10 minutes.
Stir about ¼-½ teaspoon salt into the yogurt along with 1-2 teaspoons lemon juice. Taste and adjust seasoning.
Remove sheet pan from the oven, sprinkle on remaining lemon juice and herbs, and serve with yogurt sauce.