Preheat oven to 375 degrees F. Thoroughly wash and dry sweet potatoes. Cut in half crosswise, then in quarters lengthwise. Place potatoes in a mixing bowl, drizzle with 2 tablespoons olive oil and sprinkle with salt, pepper, and smoked paprika. Drizzle remaining tablespoon oil in a baking dish and add potatoes in a single layer. Bake until soft, 35–40 minutes.
Potatoes are done when the tip of a knife slides in easily. Place on a serving platter. Drizzle remaining oil from the baking dish over the potatoes, along with a pinch of salt and pepper. Roughly chop rosemary leaves and parsley and sprinkle on top to garnish.