Prepare the Streusel Filling:
In a medium bowl, combine flour, brown sugar, cinnamon, and salt.
Work in the softened butter until small clumps form. Use your fingers to mix. Refrigerate the streusel while you prepare the cookies.
Preheat Oven:
Preheat oven to 400°F (200°C). Line two baking sheets with parchment paper or silicone baking mats. Set aside.
Combine Dry Ingredients:
In a large bowl, combine all-purpose flour, cake flour, cornstarch, cinnamon, baking soda, baking powder, and salt. Set aside.
Cream Butter and Sugars:
In the bowl of a stand mixer fitted with a paddle attachment, cream the cold cubed butter, brown sugar, and white sugar for 1-2 minutes until smooth.
Add Wet Ingredients:
Add the egg, egg yolk, and vanilla extract. Mix until combined, scraping down the sides of the bowl as needed.
Mix in Dry Ingredients:
Gradually add the dry ingredient mixture to the wet ingredients, about 1/4 cup at a time. Mix until just incorporated.
Shape and Fill Cookies:
Scoop and roll the cookie dough into 8 large balls (or smaller, if desired).
Place the dough balls onto the prepared baking sheets.
Make an indent in each cookie using your thumb or the end of a utensil. Fill each indent with about 1 tablespoon of the chilled streusel.
Bake the Cookies:
Bake for 9-11 minutes, or until the edges are set and lightly golden. Be careful not to overbake! The cookies will continue to bake on the sheet after being removed from the oven.
Optional: To get perfectly circular cookies, immediately after removing them from the oven, use a circular cookie cutter or glass to gently swirl the edges of each cookie.
Cool the Cookies:
Let the cookies rest on the baking sheet for 5 minutes, then transfer them to a wire rack to cool completely.
Make the Icing:
In a small bowl, whisk together melted butter, heavy cream, powdered sugar, vanilla, and a pinch of salt until smooth.
Once the cookies have cooled, drizzle the icing over the tops. Enjoy!