Prepare the oven and pan. Preheat the oven to 350°F. Line a 9x5-inch loaf pan with parchment paper, leaving some overhang. Place a parchment-lined sheet pan on the oven rack below to catch any drips.
Make the apple filling. Peel, core and finely dice the apples. Melt 2 tablespoons butter in a skillet over medium-low heat. Add the apples, sugar, cinnamon, lemon juice and 1 tablespoon water. Cover and cook for 8–10 minutes, stirring occasionally, until tender.
Thicken the filling. Whisk the cornstarch with 1½ tablespoons water until smooth. Stir the slurry into the apples and continue cooking until the mixture bubbles and thickens. Remove from the heat and allow to cool while preparing the biscuits.
Prepare the cinnamon sugar. Place the melted butter in a shallow bowl. Combine the sugar and cinnamon in a separate shallow bowl.
Separate the biscuits. Carefully split each flaky biscuit into two thinner rounds (splitting through its layers) to create approximately 16 thinner biscuit rounds.
Coat the biscuits. Dip each biscuit round into the melted butter, coating both sides, then immediately coat generously in cinnamon sugar.
Build the stacks. Place a spoonful of apple filling over one coated biscuit. Top with another coated biscuit and gently press down. Continue alternating biscuits and apple filling to create stacks of about 4 biscuit rounds each.
Fill the loaf pan. Turn each stack onto its side and arrange it upright in the prepared loaf pan so the biscuit layers stand vertically. As you add each new stack, spoon a little apple filling between the stacks so every biscuit layer has apple filling between it. Repeat until the pan is comfortably filled, being careful not to overcrowd it.
Make the crumb topping. Combine the flour, sugar and cinnamon. Using a fork, work in 3 tablespoons softened butter. Add additional butter gradually as needed, just until loose crumbs form. Do not overmix into a dough. Add a little additional flour if needed.
Top the loaf. Sprinkle the crumb mixture generously over the assembled loaf.
Begin baking. Loosely tent with foil and bake at 350°F for 30 minutes. Remove the foil and continue baking for another 20 minutes.
Check for doneness. Beginning at the 50-minute mark, check the biscuit layers near the center. If the dough remains wet or underbaked, continue baking in 10-minute increments until completely cooked through. Loosely replace the foil if the top becomes too dark. Total baking time can range from approximately 60–85 minutes.
Make the icing. Beat the softened butter and cream cheese until smooth. Add the powdered sugar, vanilla and salt and whisk until creamy. Add milk a small splash at a time until thick but drizzleable.
Cool and serve. Let the bread cool in the pan for about 15 minutes. Lift it from the pan using the parchment, drizzle generously with cream cheese icing and serve warm.