Preheat your oven to 350°F (175°C) and generously grease a 9×5-inch loaf pan.
In a medium bowl, combine the granulated sugar, cinnamon, and nutmeg to create your cinnamon-sugar mixture.
Peel and dice your apples into small, roughly ¼-inch cubes, then toss them with 2 tablespoons of your cinnamon-sugar mixture.
Open the cans of biscuit dough and cut each biscuit into quarters. Working with about 8-10 pieces at a time, toss them in the melted butter, then immediately roll them in the cinnamon-sugar mixture.
Begin layering in your prepared loaf pan: start with half the coated dough pieces, then half the apple mixture, followed by remaining dough pieces and finally the remaining apples. If your apples are particularly juicy, sprinkle 1 tablespoon of all-purpose flour over them to absorb excess moisture.
Bake in your preheated oven for 35-40 minutes, or until the top is deeply golden and a toothpick inserted into the center comes out clean. If the top begins to brown too quickly, loosely cover with aluminum foil after 25 minutes of baking.
While the bread is baking, whisk together the powdered sugar, 2 tablespoons of milk, vanilla extract, and salt in a small bowl. The glaze should be thick but pourable – add more milk a teaspoon at a time if needed to reach the desired consistency.
Allow the bread to cool in the pan for 10 minutes before carefully inverting onto a wire rack, then flipping right-side up onto your serving plate. While the bread is still warm (but not hot), drizzle with the prepared glaze, allowing it to seep into all the nooks and crannies.