Cut the brioche into 1-inch (2.5 cm) cubes and leave it out overnight to dry. If short on time, bake the cubes at 300 °F (150 °C) for 10 minutes until lightly dry to the touch.
8 oz (225 g) brioche
For the custard, whisk together the milk, cream, sugars, melted butter, vanilla, eggs, cinnamon, apple pie spice, and salt until smooth. Set aside while you make the caramel-style sauce.
1 cup (240 ml) milk, 1 cup (240 ml) heavy cream, ⅛ cup (25 g) granulated sugar, ⅛ cup (25 g) light brown sugar, 2 tbsps (28 g) unsalted butter, 1 tsp (5 ml) vanilla extract, 4 large eggs, 1 tsp (5 g) ground cinnamon, 1 tsp (5 g) apple pie spice, ⅛ tsp (0.5 g) kosher salt
For the caramel-style sauce, melt the butter in a large skillet over medium heat. Stir in the flour and salt and cook for 1 minute to remove the raw flour taste. Add the brown sugar, apple pie spice, and cinnamon, stirring until smooth and thick. Scoop out 1/2 cup (120 mL) now and set it aside for drizzling later. If you forget to reserve it, lift the apples out with a slotted spoon after cooking and measure out 1/2 cup (120 mL) of sauce without fruit.
8 tbsps (115 g) unsalted butter, ¼ cup (30 g) all-purpose flour, ¼ tsp (1.25 g) kosher salt, 1½ cups (300 g) light brown sugar, 2 tsps (10 g) apple pie spice, 1 tsp (5 g) ground cinnamon
For the apples, add the diced Granny Smiths and water to the caramel-style sauce remaining in the skillet. Simmer over low heat for 10–15 minutes, stirring, until the apples are tender and coated. The tart apples keep the sweetness balanced.
5 Granny Smith apples, 1 cup (240 ml) water
To assemble, grease an 8x8-inch (20x20 cm) or 9x9-inch (23x23 cm) baking dish. Layer one-third of the brioche, then one-third of the caramel apples. Repeat two more times.
Pour the custard evenly over the top, pressing the bread down with the back of a spoon so every piece is soaked. Pressing it down helps the custard bake evenly from edge to center.
Bake at 350 °F (175 °C) for 35–45 minutes, until the top is golden and the center has a slight wobble.
Warm the reserved caramel-style sauce over low heat, thinning with a splash of water if needed, and drizzle over the pudding before serving.