Combine all dough ingredients except melted butter in the bowl of a stand mixer fitted with a dough hook*. With the mixer on low speed, slowly add 2 Tablespoons melted butter. Increase speed to medium and mix until a shaggy dough forms.
Transfer the dough to a smooth work surface and knead by hand until a smooth dough forms. The dough should be smooth and slightly tacky, but not sticky. If needed, add more milk or flour (1 Tablespoon at a time) until you reach the desired consistency.
Transfer the dough to a large, greased bowl and cover with plastic wrap. Let rise 60-90 minutes, or until doubled in size.
While the dough rises, make the filling. In a small skillet over medium heat, melt 1 Tablespoon butter (the remaining softened butter will be used to assemble the layers). Add the diced apples to the skillet and cook, stirring occassionally, until softened, about 3-4 minutes. Remove from heat and stir in 1 teaspoon lemon juice. Set aside.
Grease a 9x5-inch loaf pan and set aside**. In a small bowl, combine the brown sugar, cinnamon and nutmeg. Stir until combined and set aside.
After the rise, turn the dough onto a smooth work surface and divide into 10 roughly equal-sized pieces. This does not have to be exact and the irregularity is part of the charm! Flatten each piece with the palm of your hand into an oval shape, approximately 4 inches in diameter. Spread with softened butter, then sprinkle with the brown sugar mixture and add apples to half of the oval.
Fold the piece in half (like a taco), then transfer to the prepared loaf pan, fold-side down on the bottom of the pan. Repeat with the remaining pieces of dough until the pan is filled.
Cover the pan with plastic wrap and let rise 30-45 minutes until puffed.
Preheat the oven to 350℉.
Bake for 15 minutes, then tent with aluminum foil and bake for an additional 20-25 minutes until golden brown. I highly recommend placing a baking sheet on the rack below the loaf to catch any drips that may happen! Use a kitchen thermometer to make sure the laf if fully baked. When finished, the loaf will reach an internal temperature of 200 degrees (F). Let the loaf cool in the pan for 10 minutes, then transfer to a cooling rack to cool fully.
While the loaf cools, make the glaze. In a small bowl, whisk together the powdered sugar, vanilla extract and milk until smooth. Spoon the glaze over the bread before serving.
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Notes
*This recipe can be made without a stand mixer. To do so, mix the dough in a large mixing bowl with a wooden spoon, then knead by hand. **If you are doubling or tripling this recipe, use 2 (for doubling) or 3 (for tripling) 9x5-inch loaf pans. Continue with directions as written for each loaf. To make this recipe with active sourdough starter, replace the sourdough discard with active starter (200g). You will also need to increase the rise times.