In a large mixing bowl, whisk together 2 cups of the flour, the sugar, the activated yeast, and salt. Set aside. In a separate large bowl, whisk together the eggs and set aside.
When dough is almost finish rising, peel and chop your apples. Punch down the risen dough and add 2 tablespoons of flour into the dough, kneading with your hands. Cover with a kitchen towel and let rest for 5 minutes.
Turn dough out onto a lightly floured workspace. Once finished rolling, the dough should be 12 inches tall and about 20 inches long. Brush the brown butter evenly over the dough. Sprinkle with cinnamon sugar mixture, then sprinkle evenly with apples.
You’ll have six stacks of six squares. Layer the dough squares in the loaf pan. You don't want them to be super crowded in there. I ended up discarding a few dough squares. Stuff some apples down into the dough if you lost some in the process. Place a kitchen towel over the pan and let rise again in warm place for 30 to 45 minutes or until almost doubled in size.
Preheat oven to 350℉. Bake loaf for 35-40 minutes, until the top is very golden brown. You want to make sure the top is super golden, to ensure the middle is completely cooked through. Remove from the oven and allow to rest for 20 to 30 minutes.
Run a butter knife around the edges of the loaf pan to loosen the bread and invert onto a plate or cutting board. Place a cake plate on top of the upside down loaf, and carefully invert so it’s right side up. Spread with desired amount of cream cheese icing. DEVOUR.
If you want to make the dough the night before, you can. Rise the dough until doubled in size (through step 6). Then, refrigerate the dough overnight for use in the morning. In the morning, let the dough rest for 30-40 minutes before rolling out.