Preheat the oven to 350℉ (177℃). Line baking sheet pans with silicone baking mats or parchment paper.
In a mixing bowl, whisk together the cake flour, baking powder, and salt. Set aside.
In the bowl of a stand mixer fitted with a paddle attachment or in a large mixing bowl with an electric hand mixer, cream together the unsalted butter, vegetable oil, and granulated sugar until it is light, pale, and creamy. Add in the eggs, vanilla extract, and almond extract and mix until smooth.
Add in half of the flour mixture and mix on low speed until mostly combined. Pour in the milk and mix until smooth. Add in the remaining flour mixture and mix on low speed until a soft cookie dough forms. Fold in the rainbow sprinkles.
Portion the cookie batter using a large cookie scoop (3 tablespoons). Place the cookie dough on the prepared baking sheet pans, allowing room for spreading. If desired, sprinkle additional rainbow sprinkles onto the cookies before baking.
Bake the cookies for about 12 minutes until the cookies are puffed up and set, but not brown on the edges. Transfer the cookies to a wire rack to cool completely.