How to Make It
In a large saucepan, cover the potatoes with 2 inches of water and bring to a boil. Cook over moderate heat, partially covered, until the potatoes are just barely tender, 12 to 14 minutes. Drain the potatoes. Clean and dry the saucepan.
Add 1/2 cup of the sugar to the cleaned saucepan and cook over moderate heat, swirling the pan occasionally, until the sugar has melted, about 4 minutes. Continue adding the sugar in 1/2 cup increments, melting each addition before adding the next, until all the sugar has melted to a light amber color. Reduce the heat to low and stir in the butter, 1 piece at a time.
Return the potatoes to the saucepan. The melted sugar will firm up; gently stir until the caramel is smooth again. Simmer over low heat, stirring occasionally, until the potatoes are coated in caramel (a layer of caramel will remain in the bottom of the pan), about 20 minutes more. Season the potatoes with salt. Using a slotted spoon, transfer the potatoes to a bowl and serve.