Prepare the loaf pan. Line a 9×5-inch loaf pan with parchment paper, leaving some overhang along the longer sides to make removing the baked babka easier. Lightly grease any exposed areas of the pan if necessary.
Roll out the dough. Remove the chilled sourdough brioche dough from the refrigerator and transfer it to a lightly floured work surface. Using a rolling pin, roll the dough into a rectangle measuring approximately 10×13 inches. Aim for an even thickness throughout so the babka bakes uniformly.
Add the cinnamon filling. Spread the prepared brown sugar cinnamon filling evenly across the surface of the dough, leaving approximately a ½-inch border along the edges. Use an offset spatula or the back of a spoon to distribute the filling without pressing too firmly into the dough.
Add the apples. Evenly distribute the cooled, diced apples over the cinnamon filling. Gently press the apples into the filling to help them stay in place when rolling the dough. Avoid piling the apples too thickly in any one area.
Roll into a log. Starting from one of the longer edges of the rectangle, carefully roll the dough into a tight log, keeping the apples and cinnamon filling tucked inside as you go. Pinch the seam gently to seal the dough.
Chill the log. Transfer the rolled dough to a parchment-lined baking sheet or cutting board and place it in the refrigerator for approximately 20 minutes. This important step allows the butter in the cinnamon filling to firm up, making it easier to slice and twist the babka without the filling spilling out.
Slice the dough. Remove the chilled log from the refrigerator and place it seam-side down on a cutting board. Using a sharp serrated knife, carefully slice the log in half lengthwise, creating two long pieces with the layers of apple and cinnamon filling exposed.
Twist the babka. Position the two halves next to each other with the cut sides facing upward. Carefully twist the two pieces together, crossing one over the other to create the signature braided babka appearance. Keep the cut sides facing upward as much as possible to showcase the beautiful layers of dough and filling. Gently pinch the ends together to help secure the twist.
Transfer to the loaf pan. Carefully lift the twisted babka and place it into the prepared loaf pan. Gently tuck the ends underneath if necessary to help the dough fit inside the pan. It is normal for some of the cinnamon filling or apple pieces to shift slightly during this process.
Second rise. Loosely cover the loaf pan with plastic wrap or a clean kitchen towel and allow the dough to rise in a warm location for approximately 1–3 hours, or until noticeably puffy and risen toward the top of the pan, ideally within about an inch of the rim. Depending on the temperature of your kitchen, this rise may take longer. Again, focus on the appearance of the dough rather than following the clock exactly.