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 smooth and slightly tacky but not sticky. Adjust with milk or flour if needed.
Place dough in a greased large bowl, cover with plastic wrap, and let rise 60-90 minutes until doubled in size.
While the dough rises, melt 1 Tablespoon butter in a small skillet over medium heat. Add diced apples and cook, stirring occasionally, until softened about 3-4 minutes. Remove from heat, stir in lemon juice, and set aside.
Grease a 9x5-inch loaf pan and set aside. In a small bowl, combine brown sugar, cinnamon, and nutmeg and set aside.
After rising, turn dough onto a smooth surface and divide into 10 roughly equal pieces. Flatten each into an oval about 4 inches in diameter.
Spread each piece with softened butter, sprinkle with brown sugar mixture, and add apples to half the oval. Fold in half and place fold-side down into the prepared loaf pan. Repeat until pan is full.
Cover the pan with plastic wrap and let rise 30-45 minutes until puffed.
Preheat oven to 350℉.
Bake bread for 15 minutes, then tent with foil and bake an additional 20-25 minutes until golden and internal temperature reaches 200℉.
Let cool in pan 10 minutes, then transfer to a rack to cool completely.
Whisk powdered sugar, vanilla extract, and milk in a small bowl until smooth. Drizzle glaze over bread before serving.