Raise the oven to 350°F and place a rack in the center. Grease the 9x13-inch dish with 1 tablespoon butter. Melt 1/4 cup butter and cool it for 5 minutes. Take the milk and cream out of the fridge 15 minutes ahead.

Whisk the eggs, 3/4 cup granulated sugar, and 1/4 cup brown sugar for 1 minute. Whisk in the milk and cream slowly, then the cooled butter, vanilla, cinnamon, nutmeg, and salt, until the custard looks smooth and pale gold.

Add the dried cubes and raisins. Fold 8 to 10 times with a large spatula, until every cube looks coated and no dry bread shows.

Let the bowl sit for 20 minutes, pressing the cubes down once at 10 minutes, until only a thin pool of custard remains at the bottom.

Scrape the mixture into the greased dish, level it, and sprinkle on 1 tablespoon granulated sugar, until the surface looks even.

Bake on the center rack for 50 to 60 minutes, rotating the dish 180 degrees at 25 minutes. If the top darkens early, tent loosely with foil for the last 10 minutes. The top should be deep golden and the center should barely jiggle.

Slide an instant-read thermometer into the center, where it must read 160°F. If lower, bake in 5 minute increments. A knife near the middle should come out with moist crumbs, not wet egg.

Rest the dish on a wire rack for 15 minutes, until the edges pull slightly from the sides.

Melt 1/4 cup butter in a 2-quart saucepan over medium heat. Stir in 1/2 cup brown sugar and 1/2 cup cream, boil gently for 2 minutes, then remove from the heat and add 1 teaspoon vanilla and a pinch of salt, until the sauce looks glossy and coats a spoon.

Cut the bread pudding into 12 squares, 3 rows by 4 rows, and spoon the warm sauce over each one.