Place butter in a medium sauce pan over medium high heat. Stir butter and heat until the butter turns a golden brown and smells like toffee. Set aside to cool to room temperature.
Pre heat oven to 350 degrees and prepare baking sheet with parchment paper or silicone baking mat.
In a large bowl, or bowl of a stand mixer, mix together cooled butter and sugars on medium speed. Add eggs, sourdough starter discard, and vanilla extract and blend until smooth.
Add dry ingredients to the wet ingredients and mix until all ingredients are combined.
With a 1 Tablespoon cookie scoop, spoon cookie dough onto baking sheet. For best results, press dough ball down to form cookies. This helps to make them all uniform. Bake cookies for about 8 minutes. (Baking time can vary with each oven.)
Let cookies rest on pan for 1-2 minutes. Then place on a wire rack to cool.
While cookies are cooling start mixing together the filling recipe.
Cut up butter and place in a stand mixer with a paddle attachment. Mix on medium-high speed until butter is whipped and smooth. Add in powdered sugar, vanilla, and heavy whipping cream. Beat on low speed to start and then increase speed once the powdered sugar is incorporated. Use a spatula to scrape sides of the bowl to get all ingredients combined.
Once cookies are cooled you can start spreading the filling onto half of the cookies. Then simply place the remaining cookies on top of the creamy filling and enjoy your delicious treat!