Preheat oven to 325℉. Line two 9x13-inch baking pans (quarter sheet pans) with parchment paper. Set aside.
In the bowl of a stand mixer fitted with a paddle attachment (or using an electric hand mixer), cream together butter, oil, sugar, and brown sugar until smooth and creamy, about 5 minutes. Scrape down sides of bowl as needed.
Add in eggs and vanilla. Continue to mix on low-medium speed until well combined. Scrape down sides of bowl as needed to ensure thorough mixing.
In another bowl, whisk together flour, baking powder, baking soda, and salt. Add dry flour mixture to the mixing bowl. Mix on low speed just until there are no longer any dry streaks of flour.
Use a spatula to fold in sprinkles until distributed through cookie batter.
Divide cookie batter equally between the two prepared baking pans. Use a mini offset spatula to spread cookie dough into an even layer. If desired, distribute additional sprinkles over the top of cookie dough.
Bake in the center rack of oven for 16-18 minutes until the edges are barely set. The cookies will look underdone. Remove from oven and let cookies cool in the pan. Run an offset spatula along the edges of the cookie to loosen from pan. Keep cookie sheet in pan.
Cool cookie sheets to room temperature. They will be fragile at this point.*