Add flour, 1/4 cup sugar, 1/4 cup brown sugar, 1/2 tsp. cinnamon, and yeast to the bowl of a stand mixer fitted with a dough hook. Mix until combined on low speed.
Add eggs, one at a time, mixing for 30 seconds between each.
Add butter, one tablespoon at a time. Add salt and scrape down sides with spatula.
Turn speed to medium and mix for 10 minutes until dough is smooth.
Coat large bowl with nonstick spray. Place dough inside. Place tea towel or plastic wrap on top and let rise at room temperature until doubled (up to 8 hours).
Spray two 9" x 4" loaf pans. Line bottoms with parchment paper. Set aside.
Flour baking sheet. Set aside.
Make Apple Pie Bread filling. Whisk sugar, flour, cinnamon, nutmeg, and salt together in medium bowl. Add apples and work with hands until apples are completely coated and mixture is wet. Set aside.
Combine 4 tsp. cinnamon and remaining 1/2 cup sugar in small bowl. Set aside.
Sprinkle counter with flour. Cut dough into two equal pieces and roll the first into 10" x 12" rectangle.
Top rectangle with 1/2 cinnamon sugar mixture. Spread 1/2 apple pie filling mixture on top. Dot with butter.
Starting from the edge closest to you, roll dough from bottom to top. Wet the top edge with water to seal. Place on floured baking sheet and put in freezer for 10 minutes. Repeat with other half of apple pie bread dough.
Remove roll from freezer and, starting 1" from top, slice in half lengthwise. Twist two halves around each other, keeping filling on the outside. Tuck the roll inside the loaf pan. Repeat.
Place tea towel on top of each loaf pan. Let rise for 90 minutes.
Preheat oven to 375° F. Bake on middle rack for 30 minutes or until golden.
Let Apple Pie Bread cool on cooling rack in loaf pan.
Make the sugar syrup. Combine sugar and water together in a small saucepan. Heat on medium until sugar has dissolved. Brush sugar syrup over baked bread. Let cool completely before adding Honey Caramel Sauce.