Preheat oven to 350 degrees F.
Butter a 2 to 3 quart baking dish and evenly spread out the bread cubes.
In a saucepan combine the half-and-half, butter, salt and vanilla and heat until hot over moderate heat. In a bowl whisk together sugar, eggs, and yolks and add hot half-and-half mixture in a stream, whisking constantly. Pour mixture over bread cubes. Bake pudding in middle of oven about 40 to 45 minutes, or until puffed and golden. Serve warm with vanilla ice cream.
Adapted from a recipe in Gourmet Magazine