In the bowl of a stand mixer or a large mixing bowl (with a hand mixer), beat butter and sugars for 2-3 minutes until light and fluffy. Add egg, vanilla and almond, mix until combined. Add the flour, baking soda and salt, mix until a soft dough forms.
Wrap the dough in plastic wrap and chill for 2 hours.
20 minutes before removing the dough from the refrigerator, prepare the filling. In a small saucepan over medium heat, add the butter. Brown the butter by letting it pop, foam and then form tiny brown speckles on the bottom of the saucepan. Remove from the heat and allow to cool in a separate bowl.
In a small mixing bowl combine the sugar, cinnamon, and cornstarch.
Roll the dough into a 12-inch by 16-inch rectangle. I like to roll it out on a lightly floured silcone baking mat (the half sheet pan size is the correct size). Brush the butter over top, then sprinkle with cinnamon sugar mixture over top, patting gently so it sticks.
Using the baking mat to help, roll the dough into a tight log. Press the dough to seal the end of the roll. Wrap in plastic wrap and freeze for 1 hour.
Preheat oven to 375 degrees. Line a baking sheet with parchment paper or a silicone mat.
Slice the log into ¼” thick slices. Place 12 on a baking sheet at a time. Bake for 10-12 minutes, remove from the oven and allow to cool on the sheet for 3 minutes before transferring to a wire rack to cool completely.
While the cookies are cooling, in a small mixing bowl whisk together the powdered sugar, water or milk, and vanilla. Drizzle over the cookies and allow to set before serving or storing.