Preheat your oven to 350°F (175°C). Grease and flour a 9-inch round cake pan.
In a large mixing bowl, whisk together the flour, granulated sugar, baking powder, and salt until well combined.
In a separate bowl, beat the eggs. Add the melted butter, milk, and vanilla extract, stirring until smooth.
Pour the wet ingredients into the dry ingredients and stir gently until just combined. Do not overmix.
Fold in the diced apples, ground cinnamon, and ground nutmeg until evenly distributed throughout the batter.
Pour the batter into the prepared cake pan and spread it evenly.
In a small bowl, combine the softened butter, brown sugar, and cinnamon for the topping. Mix until it forms a crumbly texture.
Sprinkle the butter and sugar topping evenly over the batter in the cake pan.
Bake in the preheated oven for 40 to 45 minutes, or until a toothpick inserted into the center comes out clean.
Remove the cake from the oven and allow it to cool in the pan for 10 minutes.
Transfer the cake to a wire rack to cool completely before serving.