Preheat the oven to 350°F (175°C). Line 3 baking sheets with parchment paper and set aside.

In the bowl of a stand mixer fitted with the paddle attachment, cream together the butter, oil, granulated sugar, and powdered sugar on medium speed until light and fluffy.

Add the eggs one at a time, beating well after each addition. Scrape down the sides of the bowl as needed.

Mix in the vanilla extract and sour cream until just combined.

Add the baking soda, baking powder, salt, and flour. Mix on low speed until just combined, ensuring no streaks of flour remain. Do not overmix.

Scoop the dough into 3-tablespoon-sized portions and roll into balls. Place them several inches apart on the prepared baking sheets.

Using a flat surface like a pancake spatula or the bottom of a cup, press down each ball slightly to about ½-inch thickness.

Bake the cookies for 10-12 minutes until just set, avoiding browning.

Let the cookies cool on the baking sheets for a few minutes before transferring to a cooling rack to cool completely.

Preheat the oven to 350°F (175°C) and line a baking sheet with parchment paper.

In a medium bowl, combine the brown sugar, granulated sugar, flour, citric acid, and salt. Use a fork to mix until well combined.

Add the melted butter and stir until the mixture forms chunky clumps. Stir in the rainbow sprinkles.

Spread the crumb mixture onto the prepared baking sheet and bake for 7 minutes. Remove from the oven, gently stir the mixture with a fork, then bake for an additional 5 minutes.

Let the crumb mixture cool completely before using.

In a medium bowl using an electric hand mixer, cream together the butter and cream cheese on medium speed for about 2 minutes. Scrape down the sides and bottom of the bowl and beat for another 2 minutes.

Gradually add the powdered sugar, then mix in the vanilla extract, citric acid, and salt. Mix on low speed until combined, then increase to medium speed and beat for 2-3 minutes until light and fluffy.

Once the cookies are completely cooled, frost them using a piping bag or a plastic bag with a medium-sized hole cut at the tip.

Sprinkle the crumb topping and additional rainbow sprinkles over the frosted cookies.

Serve the cookies at room temperature or chilled.