In a large mixing bowl or the bowl of a stand mixer, combine the active sourdough starter, warm milk, granulated sugar, and egg. Mix well until combined.

Add the all-purpose flour and salt. Mix with a spoon or the dough hook on low speed until a shaggy dough forms. Cover the bowl and let it rest for 30 minutes (autolyse).

After resting, add the softened butter, one tablespoon at a time, incorporating each piece before adding the next. Knead the dough using your hands or the stand mixer on medium-low speed for 10-15 minutes, or until the dough is smooth, elastic, and passes the windowpane test.

Transfer the dough to a lightly oiled clean bowl, turning once to coat. Cover with plastic wrap or a damp towel and bulk ferment at room temperature (72-78°F / 22-25°C) for 4-6 hours, performing a set of coil folds every hour for the first 3 hours. Alternatively, for a deeper flavor development, place the covered bowl in the refrigerator for 8-12 hours for a cold bulk fermentation.

While the dough is fermenting, or during the morning of Day 2 if cold proofing, prepare the apple filling. In a medium bowl, combine the finely diced apples, light brown sugar, ground cinnamon, all-purpose flour, and lemon juice. Mix thoroughly to coat the apples. Set aside.

Lightly grease a 9x5 inch loaf pan and line it with parchment paper, leaving an overhang on the long sides to easily lift the bread out later.

Lightly flour a clean work surface. Gently turn the dough out onto the surface. Roll the dough into a rectangle approximately 10x16 inches (25x40 cm).

Spread the apple filling evenly over the entire surface of the dough, leaving about a 1/2-inch border along one of the long edges.

Starting from the long edge opposite the clean border, tightly roll the dough into a log. Pinch the seam closed.

Using a sharp knife, slice the log lengthwise down the middle, creating two halves with the filling exposed. Keep the top end attached for about an inch to make twisting easier.

Gently twist the two halves together, keeping the cut sides facing up, to create a braided appearance. Carefully transfer the twisted dough into the prepared loaf pan.

Cover the loaf pan loosely with plastic wrap or a clean kitchen towel. Let the bread proof in a warm spot for 2-3 hours, or until it has visibly risen and looks puffy (it should pass the 'poke test' where a gentle poke leaves a slight indentation that slowly springs back).

Preheat your oven to 375°F (190°C) about 20 minutes before the end of the proofing time.

Bake the Sourdough Apple Fritter Bread for 45-55 minutes, or until deeply golden brown and an internal temperature of 200-205°F (93-96°C) is reached. If the top browns too quickly, tent loosely with aluminum foil.

Remove the bread from the oven and let it cool in the pan for 10-15 minutes before carefully lifting it out by the parchment paper overhang and transferring it to a wire rack to cool completely.

While the bread cools, whisk together the powdered sugar, milk, and vanilla extract in a small bowl until smooth. Adjust milk amount for desired consistency.

Once the bread has cooled to just warm, drizzle the glaze generously over the top. Let the glaze set for a few minutes before slicing and serving. Enjoy!