For the topping: Preheat oven to 300 degrees F. Line a baking sheet with parchment paper and set aside.
Whisk egg white in a medium bowl until frothy (reserve yolk for the pudding). Add brown sugar, cinnamon, salt and cayenne pepper. Add almonds and toss to coat. Transfer to prepared baking sheet. Bake for 20 minutes, then allow to cool completely at room temperature on the baking sheet. Break up into pieces.
For the pudding: Meanwhile, grease a 2-quart baking dish.
Whisk whole eggs and egg yolks (including reserved yolk) together in a large bowl. Add milk, granulated sugar, vanilla, cinnamon, salt and almond extract and whisk until blended, then mix in the cooked rice. Transfer to prepared baking dish.
Place baking dish in a larger roasting pan. Create a warm water bath by adding hot water to the large pan until it reaches about 1 inch up the sides of the smaller baking dish.
Cover with aluminum foil and bake for 1 hour. Remove foil and bake until set, another 10 to 20 minutes.