1 cup (2 sticks) unsalted butter, at room temperature
1 ½ cups granulated sugar
2 large eggs
1 teaspoon cake batter extract
½ teaspoon pure vanilla extract
2 cups cake flour
1 cup all-purpose flour
1 teaspoon baking soda
1 teaspoon kosher salt
½ cup rainbow sprinkles, plus more for sprinkling
9 ounces (2 sticks plus 2 tablespoons) unsalted butter, at room temperature
1 ½ teaspoons pure vanilla extract
3 ¾ cups powdered sugar
1 ½ tablespoons whole milk
To make the confetti cookies: Preheat the oven to 350°F. Line two baking sheets with parchment paper.
In a stand mixer fitted with the paddle attachment, cream the butter and sugar on medium-high speed, until light and fluffy, about 1 to 2 minutes. Add the eggs, one at a time, and mix until thoroughly incorporated, then add the cake batter extract and vanilla and continue mixing. Slowly add both flours, the baking soda, baking powder, and salt. Mix until all the dry ingredients are incorporated, then mix in the rainbow sprinkles.
Using a 1-ounce scoop, portion the cookie dough into balls and place at least 2 inches apart on the prepared baking sheets. Sprinkle the tops with a few more sprinkles.
Bake, swapping the placement of the pans halfway through, until the edges start turning a golden color, 10 to 12 minutes. Let the cookies cool on the baking sheets for at least 5 minutes, then transfer to wire racks to cool completely.
To make the filling: In a stand mixer fitted with the paddle attachment, cream the butter on high speed until light and fluffy, 3 to 4 minutes. Beat in the vanilla.
Reduce the speed to low and slowly beat in the powdered sugar, about ¼ cup at a time, then beat in the milk. When the mixture is smooth, increase the speed to medium, mixing until thoroughly combined and fluffy, about 2 more minutes.
Set the cookies up in pairs, with the bottom of one of them facing up. Using a small scoop, place about 1 ½ tablespoons of the filling on the bottom of the upside-down cookie. Place the second cookie on top, right side up, and sandwich them together, pressing just enough to spread the filling to the edges. Repeat to make the rest of the sandwiches.
Store in an airtight container at room temperature for up to 5 days.