In a small bowl, combine warm water and active dry yeast. Stir gently and let sit for 5 minutes until foamy.
In a large mixing bowl, whisk together the flour, sugar, salt, ground cinnamon, and ground nutmeg.
In a separate bowl, whisk the warm milk, egg, and melted butter until combined.
Add the yeast mixture and the milk mixture to the dry ingredients. Stir with a wooden spoon until a rough dough forms.
Turn the dough out onto a lightly floured surface and knead for about 8-10 minutes until the dough is smooth and elastic.
Gently knead in the chopped apple pieces until evenly distributed throughout the dough.
Place the dough in a lightly greased bowl, cover with a clean kitchen towel or plastic wrap, and let rise in a warm place for 1 hour or until doubled in size.
Preheat the oven to 350°F (175°C).
Punch down the dough to release air, then shape it into a loaf and place it in a greased 9×5-inch loaf pan.
Cover the loaf pan and let the dough rise again for 30 minutes until it has risen just above the edge of the pan.
Bake the bread in the preheated oven for 30-35 minutes, or until the top is golden brown and a toothpick inserted into the center comes out clean.
Remove the bread from the oven and let it cool in the pan for 10 minutes, then transfer to a wire rack to cool completely before slicing.