Preheat oven to 350°F.
Line a 9x13-inch baking pan with parchment paper.
In the bowl of a stand mixer, cream together butter and oil. Add granulated sugar and brown sugar and beat until creamy. Add in the egg and vanilla and continue to mix until smooth.
In a small bowl, whisk together all-purpose flour, cake flour, baking soda, baking powder, and salt. Add the dry ingredients into the creamed mixture at low speed. Mix until the dry has been incorporated. Add the chocolate chips and sliced almonds. Mix until just combined.
Transfer batter to the prepared baking pan. Press into an even layer using parchment paper. Bake for 20-25 minutes, until lightly browned. Let cool completely on a rack before unmolding. Be sure to run a knife around the edges before inverting. Peel off parchment paper and cut into desired servings.