Preheat the oven to 375°F (190°C).

In a bowl, sift together the all-purpose flour, cake flour, baking powder, and baking soda.

In a large bowl, cream together the softened butter, white sugar, and brown sugar until the mixture is smooth and creamy.

Beat in the eggs one at a time, then stir in the vanilla extract until well blended.

Gradually add the sifted flour mixture to the wet ingredients, mixing until just combined.

Stir in the semi-sweet chocolate chips.

Drop rounded tablespoonfuls of dough 2 inches apart onto ungreased cookie sheets.

Bake in the preheated oven for 10 to 14 minutes, or until the edges are lightly golden brown.

Let the cookies cool on the baking sheet for a few minutes before transferring them to wire racks to cool completely.