Preheat the oven to 350°F (175°C) and line baking sheets with parchment paper. In a medium bowl, whisk together the flour, baking powder, baking soda, and salt. Set the flour mixture aside. In a large bowl, cream together the softened unsalted butter, packed light brown sugar, and granulated sugar with an electric mixer on high speed until the mixture is light and fluffy, about 2-3 minutes. Add the egg yolks, vanilla bean paste or vanilla extract, butter extract, and melted and cooled butterscotch chips to the creamed mixture. Mix on medium speed until pale and fluffy, 1-2 minutes, scraping the sides of the bowl as needed. Add the dry ingredients to the wet mixture and mix on low speed until just combined. Finally, fold in the butterscotch chips with a rubber spatula.

Using a large cookie scoop, portion the dough from Step 1 into 2-tablespoon sized balls, then arrange them 6 at a time and 2 inches apart on the prepared baking sheets. Bake the cookies for 10-11 minutes, until set but still soft in the center. Immediately after baking, use a large circular cookie cutter to gently scoot around each cookie, shaping them perfectly round. Let the cookies cool on the cookie sheet for 5 minutes before transferring to a wire rack to cool completely.

While the cookies are baking or cooling, pour the butterscotch beer or cream soda into a pot. Bring it to a simmer over medium-low heat and cook until it thickens and turns a deep golden color, about 15-17 minutes. Turn the heat down to low and stir in the softened butter until fully incorporated. Then mix in the heavy cream and a pinch of salt. Let the caramel simmer for one more minute before removing from the heat to cool. I recommend letting the caramel cool to room temperature so it’s easy to drizzle but not too runny.

In a medium bowl, whip the softened unsalted butter and salt with an electric mixer on high speed until very pale and fluffy, about 5-10 minutes. Add the melted and slightly cooled butterscotch chips and mix until combined. Sift in the powdered sugar and continue to mix until well incorporated. Finally, add the butter extract and vanilla bean paste or vanilla extract, mixing the frosting for another minute until it’s light and super fluffy. For extra flavor, I like to use vanilla bean paste instead of extract here—it gives the frosting wonderful flecks and aroma.

Once the cookies from Step 2 have completely cooled, generously spread the butterscotch buttercream frosting from Step 4 over each one using a mini offset spatula. Drizzle the cooled butterbeer caramel from Step 3 over the frosted cookies. Optionally, sprinkle with your favorite decorative sprinkles before serving.