Preheat your oven to 350°F (175°C). Grease a 9×5-inch loaf pan with butter or non-stick cooking spray. For extra insurance against sticking, you can line the bottom of the pan with a strip of parchment paper.
In a large mixing bowl, whisk together the all-purpose flour, granulated sugar, baking powder, baking soda, salt, cinnamon, and nutmeg. Ensure there are no large lumps and that the spices are evenly distributed throughout the flour mixture.
In a separate medium bowl, whisk together the apple cider, eggs, melted butter, and vanilla extract until well combined. Make sure your eggs are at room temperature so they incorporate easily with the melted butter.
Slowly pour the wet ingredients into the dry ingredients. Use a spatula to gently fold the mixture together until just combined. Be careful not to overmix, as this can make the bread tough. Gently fold in the finely diced apple pieces at the very end.
Pour the batter into the prepared loaf pan and smooth the top with your spatula. Place the pan in the center of the oven and bake for 50 to 60 minutes. The bread is done when a toothpick inserted into the center comes out clean or with just a few moist crumbs.
Allow the bread to cool in the pan for about 10 minutes. This helps the structure set. Then, carefully remove the loaf from the pan and transfer it to a wire rack to cool completely before slicing.