Position a rack in the center of the oven and set the rimmed baking sheet on it. Heat the oven to 425°F (220°C) and let it preheat for at least 15 minutes, leaving the pan bare.
Scrub the potatoes under cold running water and leave the skins on. Trim away green patches, deep eyes, or sprouts, cut into 1-inch cubes, and pat very dry on a clean kitchen towel.
Transfer the dry cubes to a large mixing bowl, drizzle with olive oil, and toss to coat. Sprinkle in the salt, pepper, garlic powder, smoked paprika, and dried thyme, then toss about 30 seconds until evenly coated.
Carefully pull the hot sheet pan from the oven, pour on the potatoes, and spread them in a single layer with a flat side down, leaving space between cubes. Roast 20 minutes without touching, then flip with a thin metal spatula and roast another 15 to 20 minutes until deep golden and fork-tender.
During the last 5 minutes of roasting, microwave the butter 20 to 30 seconds until melted, then stir in the minced garlic and chopped parsley.
Transfer the hot potatoes to the mixing bowl, pour the garlic butter over the top, and toss gently about 10 seconds to coat. Taste and add a pinch of salt if needed, then move to a wide serving platter right away.