Preheat the oven to 350°F (175°C). Grease a bundt pan with cooking spray or butter.
In a small bowl, mix together the granulated sugar and ground cinnamon. Set aside.
In another bowl, combine the diced apples, lemon juice, vanilla extract, brown sugar, and ground nutmeg. Stir until the apples are well coated.
Open the cans of biscuit dough and separate the biscuits. Cut each biscuit into quarters.
Dip each biscuit piece into the melted butter, then roll it in the cinnamon-sugar mixture until well coated.
Layer half of the coated biscuit pieces in the bottom of the prepared bundt pan. Pour half of the apple mixture over the biscuits.
Add the remaining biscuit pieces on top of the apples and then pour the rest of the apple mixture over them.
Finish by layering any remaining biscuit pieces on top.
Brush the top with the beaten egg to create a golden crust.
Bake in the preheated oven for 30-35 minutes, or until the bread is golden brown and cooked through.
Allow to cool for 10 minutes in the pan before inverting onto a serving plate. Dust with powdered sugar if desired, and serve warm.