Preheat the oven to 325°F. Grease and line an 8-inch square baking dish with parchment paper.
To make the streusel topping, combine all-purpose flour, light brown sugar, ground cinnamon, and salt. Pour in the melted butter and mix with a fork until the ingredients come together. Keep the mixture in large crumbles; do not overmix.
Toss the diced apples and the extra tablespoon of flour in a small bowl and set it aside.
Whisk the flour, baking powder, baking soda, salt, apple pie spice, and ground cinnamon in a medium bowl.
In a large mixing bowl, beat the softened butter and sugar using an electric mixer until light and fluffy. Add the egg and vanilla extract and mix to combine. Alternatively, add the dry ingredients and the sour cream, starting and ending with the dry, and mix well after each addition. Fold in the diced apples and pecans.
Pour the batter into the prepared pan and spread evenly. Sprinkle the streusel over the batter's top, covering the surface.
Bake until a toothpick inserted into the center of the cake comes out clean, about 45-50 minutes.