Begin by scrubbing the red potatoes thoroughly under cold running water to remove any dirt. Leave whole if small, or cut into halves or quarters for quicker cooking. Place potatoes in a large pot and cover with cold water. Add 1 tablespoon kosher salt. Bring to a boil over high heat, then reduce to a simmer. Cook until fork-tender, about 15-20 minutes depending on size.
Drain the potatoes well in a colander once tender but not falling apart. Allow to cool for a few minutes so butter won’t melt immediately when tossed in, helping the potatoes absorb flavors better.
Transfer warm potatoes to a mixing bowl. Add unsalted butter and let it melt over the warm potatoes as you gently toss. Sprinkle minced fresh parsley and season with additional kosher salt to taste. Toss gently but thoroughly to coat every piece with buttery herb mixture.
Serve immediately for best texture and flavor. These potatoes pair beautifully with a variety of mains and make a versatile, crowd-pleasing side.