Preheat the oven to 350°F. Generously grease a 10- to 12-cup Bundt pan with nonstick cooking spray or softened butter.
Peel, core, and finely dice the apples.
Combine the granulated sugar, cinnamon, and apple pie spice in a large zip-top bag or mixing bowl.
Cut each biscuit into quarters. Add the biscuit pieces to the cinnamon-sugar mixture in batches and toss until evenly coated.
Arrange about one-third of the coated biscuit pieces in the bottom of the prepared Bundt pan. Sprinkle with one-third of the diced apples. Continue layering the biscuit pieces and apples until everything has been added.
In a small bowl, whisk together the melted butter, brown sugar, vanilla, and salt.
Pour the butter mixture evenly over the biscuit dough and apples.
Bake for 35–40 minutes, or until the top is deeply golden and the dough in the center is fully baked. If the top begins browning too quickly, loosely cover it with foil during the last 10 minutes.
Allow the monkey bread to cool in the pan for about 10 minutes. Carefully invert the pan onto a large serving plate.
To make the glaze, whisk together the powdered sugar, milk, vanilla, and salt until smooth. Add a little additional milk if necessary to reach a drizzling consistency.
Drizzle the glaze over the warm monkey bread and serve.