Preheat oven to 350°F (175°C) and grease a 9x13 inch baking pan.
Whisk together cake flour, baking powder, baking soda, and ground cinnamon in a mixing bowl.
In a large bowl, beat butter, granulated sugar, and brown sugar until creamy.
Add vegetable oil, eggs, milk, and vanilla extract; mix until smooth.
Gradually add the dry ingredients to the wet mixture and stir until just combined.
Fold in shredded carrots and crushed pineapple gently.
Pour batter into prepared pan and bake for approximately 36 minutes or until a toothpick inserted comes out clean.
Let the cake cool for 10 minutes in the pan, then transfer to a cooling rack.
For the frosting, beat butter and cream cheese until smooth.
Gradually add powdered sugar and mix well, then stir in pineapple juice until creamy.
Once the cake is fully cooled, spread cream cheese frosting evenly over the top.
Sprinkle toasted chopped pecans on the frosting before serving.