Preheat your oven to 350°F (175°C). Grease and flour a 9-inch round cake pan to prevent sticking.

In a large mixing bowl, combine the sifted flour, 1/2 cup of granulated sugar, baking powder, baking soda, and salt. Whisk together until evenly mixed.

In another bowl, cream the softened butter and the remaining 1/2 cup of granulated sugar together using a whisk or electric mixer until light and fluffy, about 3-5 minutes. This incorporates air into the butter, helping the cake rise.

Add the eggs one at a time, mixing well after each addition. Then, mix in the sour cream and vanilla extract until fully combined.

Gradually add the dry ingredients to the wet ingredients, mixing just until combined. Be careful not to overmix, as this can lead to a dense cake.

Fold in the diced apples gently using a spatula, ensuring they are evenly distributed throughout the batter.

In a small bowl, combine the flour, brown sugar, and cinnamon. Pour in the melted butter and mix until crumbly. This will create a sweet, crunchy topping for the cake.

Pour the batter into the prepared cake pan and spread it evenly. Sprinkle the streusel topping over the batter, ensuring it is evenly distributed.

Bake in the preheated oven for 40-45 minutes, or until a toothpick inserted into the center comes out clean. This ensures the cake is fully cooked through.

Once baked, remove the cake from the oven and let it cool in the pan for about 10 minutes. Then, transfer it to a wire rack to cool completely.

Slice the cake into wedges and serve warm or at room temperature. This cake pairs wonderfully with coffee or tea.