Cover potatoes, parsnips and garlic with 1 inch of water in a 4 to 6-quart pot, then add sprig of rosemary and salt and bring to a boil, partially covered.
Reduce heat and simmer vegetables, partially covered, until very tender but not falling apart, 30 to 40 minutes.
Drain vegetables in a colander.
Discard rosemary and mash warm vegetables along with sour cream, butter, pepper, and remaining pinch of salt, to taste; stir to combine well.