1. Mix warm water, brown sugar, yeast, and melted butter in a bowl. Let the mixture sit for 5 minutes until frothy.
2. Add sea salt and flour gradually to the yeast mixture, kneading until the dough is smooth and elastic. Cover the dough and let it rise for about 1 hour in a warm place.
3. While the dough rises, prepare the filling. In a medium saucepan, cook chopped apples, cinnamon, and granulated sugar over medium heat until apples are soft. Remove from heat and stir in caramel sauce.
4. Preheat the oven to 425°F (220°C).
5. Divide the risen pretzel dough into 8 equal pieces. Roll each piece into a rectangle on a floured surface. Spread a generous amount of apple filling down the center of each piece, then roll into logs, sealing the edges tightly.
6. Shape each filled log into a pretzel shape.
7. Prepare a large pot of boiling water mixed with baking soda for dunking the pretzels. Quickly dunk each pretzel, removing after 30 seconds, then place on a parchment-lined baking sheet.
8. Brush each pretzel with beaten egg and sprinkle with coarse sea salt.
9. Bake in the preheated oven for 15-18 minutes until golden brown. Serve warm, enjoying with your favorite autumn beverage.