Step 1

Preheat oven to 375 degrees F (190 degrees C). Grease a 2-quart baking dish.

Step 2

In a mixing bowl, whisk 3 eggs, white sugar, 2 tablespoons of light brown sugar, 1/2 teaspoon of cinnamon, 1/4 cup of butter, and 3 cups of whole milk together, and gently stir in the bread cubes and raisins. Lightly spoon the mixture into the prepared baking dish.

Step 3

Bake in the preheated oven until browned and set in the middle, 50 to 55 minutes; cover the dish with foil after 30 minutes to prevent excessive browning. Let the pudding stand for 10 minutes before serving.

Step 4

For vanilla sauce, whisk 1/2 cup of light brown sugar, the flour, a pinch of cinnamon, 1 egg, 2 tablespoons of melted butter, 1 1/4 cups of whole milk,and salt together in a heavy saucepan until smooth. Heat over medium heat, whisking constantly, until thickened and the sauce coats the back of a spoon, 10 to 12 minutes. Stir in the vanilla extract. Pour sauce over warm bread pudding, or serve on the side in a bowl.