Prepare the Dough: In a large mixing bowl, whisk together 2 cups of the flour, the sugar, yeast, and salt. Set aside.
In a small bowl, whisk together the eggs and set aside.
Place the milk and butter in a small saucepan over medium-low heat, and heat, stirring occasionally, until the butter has just melted. Remove from the heat and add the water and vanilla extract. Let mixture stand until it registers 115 to 125 degrees F on an instant read thermometer.
Pour the milk mixture into the dry ingredients and mix with a spatula. Add the eggs and stir the mixture until the eggs are incorporated into the batter. The eggs will feel soupy and it’ll seem like the dough and the eggs are never going to come together. Keep stirring. Add ¾ cup of the remaining flour and stir with the spatula for about 2 minutes. The mixture will come together but be slightly sticky.
Place the dough is a large, greased bowl. Cover with plastic wrap and a clean kitchen towel. Place in a warm space and allow to rest until doubled in size, about 1 hour. (Make Ahead!>> The dough can be risen until doubled in size, then refrigerated overnight for use in the morning. If you’re using this method, just let the dough rest on the counter for 30 minutes before following the roll-out directions below.)
Prepare the Filling: In a medium bowl, whisk together the sugar and cinnamon, then stir in the chopped apple until evenly coated. Set aside.
Assemble the Bread: Deflate the risen dough and knead the remaining 2 tablespoons of flour into the dough. Cover with a clean kitchen towel and let rest for 5 minutes. On a lightly floured work surface, use a rolling pin to roll the dough into a 12 x 20-inch rectangle. Brush the melted butter across all of the dough. Spread the apple/cinnamon-sugar mixture evenly all over the dough (if there is any accumulated juices, drizzle that over the dough too).
Slice the dough (I use a pizza cutter!) into six equal-sized strips in both directions for a total of 36 squares/rectangles (they might not all be the same size/shape and that's okay). Create six stacks of six layers each. Layer the dough squares in the loaf pan cut-side up. (You can do them all in one direction or alternate them like I did.) Cover with a kitchen towel and place in a warm place for 30 to 45 minutes, or until almost doubled in size.
Bake the Bread: Preheat oven to 350 degrees F. Cover a sheet pan with foil and place on the lowest oven rack to catch any drips. Place the bread in the oven and bake for 35 to 45 minutes, until the top is very golden brown, and an instant read thermometer placed into the center of the bread reads at least 190 degrees F. (The top may be lightly browned, but the center may still be raw. A nice, dark, golden brown will ensure that the center is cooked as well.)
Remove from the oven and allow to rest for 20 to 30 minutes. Run a butter knife around the edges of the pan to loosen the bread and remove to a cutting board or serving plate. Serve warm or at room temperature. The bread is best served the day it’s made, but it can also we wrapped in plastic wrap and kept at room temperature for up to 2 days.