Instructions:

Preheat Oven and Prepare Bread: Preheat your oven to 350°F (175°C). Combine the cubed white bread and raisins in a large bowl.
Heat Milk Mixture: Combine the milk and ¼ cup of butter in a 1-quart saucepan. Cook over medium heat until the butter is completely melted (about 4 to 7 minutes).
Soak Bread: Pour the warm milk mixture over the bread and raisin mixture in the bowl. Let it stand for 10 minutes to allow the bread to absorb the liquid.
Add Remaining Pudding Ingredients: After the bread has soaked, stir in the remaining bread pudding ingredients: ½ cup of sugar, slightly beaten eggs, 1 tablespoon of vanilla, and ½ teaspoon of ground nutmeg. Mix gently until everything is well combined.
Bake the Pudding: Pour the bread pudding mixture into a greased 1 ½-quart casserole dish. Bake in the preheated oven for 40 to 50 minutes, or until the pudding is set in the center. A knife inserted near the center should come out mostly clean.
Make the Vanilla Sauce: While the bread pudding is baking, prepare the vanilla sauce. Combine the ½ cup of butter, ½ cup of granulated sugar, and ½ cup of firmly packed brown sugar in a 1-quart saucepan. Cook over medium heat, stirring occasionally, until the mixture thickens and comes to a full boil (about 5 to 8 minutes).