Heat oven to 350°F. Grease a 9x13-inch baking dish with butter.
Cube the bread and add it to the dish. If very fresh, toast in the oven 5 minutes to dry slightly.
Whisk milk, cream, beaten eggs, both sugars, vanilla, cinnamon, nutmeg, and salt until smooth.
Pour custard over the bread. Scatter raisins on top, then press gently so everything soaks. Rest 10 minutes.
Drizzle the melted butter over the surface.
Bake 40–45 minutes, until puffed, golden, and just set in the center.
Make the sauce: Whisk milk, cream, sugar, cornstarch, and a pinch of salt in a saucepan until lump-free.
Cook over medium heat, stirring, until thick and gently bubbling, 3–5 minutes. Off heat, whisk in butter and vanilla.
Cool the pudding 10 minutes. Serve warm with spoonfuls of the warm vanilla sauce.