Preheat your oven to 375°F (190°C). Grease a 2-quart baking dish with butter or cooking spray.

In a large bowl, whisk together 3 cups whole milk, eggs, sugar, vanilla, cinnamon, and salt. Gently stir in bread cubes and raisins, pressing to soak.

Transfer mixture to the prepared dish. Bake for 50–60 minutes, until pudding is set and golden on top.

While pudding bakes, melt butter in a saucepan over medium heat. Stir in brown sugar until dissolved and bubbly. Remove from heat, then whisk in heavy cream, beaten eggs, vanilla, and salt. Return to low heat, stirring until slightly thickened—do not boil.

Let pudding cool 5 minutes, then cut into squares. Drizzle generously with warm vanilla sauce and enjoy.