Whisk together the milk, salt and egg yolks. Combine the rice and milk mixture in a medium clay bram or 4-quart Dutch oven.
Distribute the butter in thin shavings over the surface. Place the bram on a baking sheet as a safeguard from spills. Cover with foil and bake for 30 minutes. Uncover and bake until a rich, golden brown crust has formed on the top and perimeter of the rice, about 1 hour more. Most of the milk should have been absorbed. Allow to sit at room temperature for 10 minutes before serving.