Place potatoes in a saucepan and cover with 1 inch of water, season with salt; bring to a boil, reduce heat to a simmer and cook until potatoes are tender, about 15 minutes.
Drain potatoes, return to saucepan with butter and milk.
Once butter melts, turn off heat and add sour cream; mash potatoes.
Season with more salt, if necessary, and pepper; stir in basil and serve.