Preheat the oven to 350°F. Grease a 9x13-inch baking dish with vegan butter or avocado oil.
In a large mixing bowl, whisk the almond milk, coconut milk, maple syrup, vanilla extract, cinnamon, nutmeg, ginger, and cornstarch until well combined.
Dice the bread into 1-inch cubes. Peel, core, and dice the apples.
Add the cubed bread and half of the chopped apples to a 9x13 casserole dish. Pour the custard over the bread and fold it together until evenly coated.
Allow the bread mixture to absorb the custard for 10–15 minutes.
Top with additional diced apples and pumpkin seeds.
Bake for 40–45 minutes until the top is golden and slightly crisp, and the bread pudding is set in the center.
Let the bread pudding cool slightly before serving. If desired, you can drizzle it with extra maple syrup or vegan caramel sauce or dust it with powdered sugar. Top with a scoop of vegan vanilla ice cream.