Add flour, salt, baking soda, and cream of tartar to a medium bowl. Whisk to combine and set aside.

Add butter to large saucepan over medium heat. Butter will begin to foam and then brown quickly. Stir constantly during entire process. Once butter begins to brown, remove from heat and pour into a medium heatproof bowl. Set aside to cool for 10 minutes.

Add light brown sugar and granulated sugar to bowl. Mix until combined. Add egg and vanilla extract and mix until combined.

Add 1/3 of the flour mixture to wet ingredients and and mix until nearly combined. Repeat with remaining thirds of flour mixture until just fully combined and no more streaks of flour are visible.

Set a piece of parchment paper on the counter. Sprinkle a little flour onto the parchment paper. Add the dough. Using a rolling pin, roll the dough into a rectangle, about 1/3 inch thick. Set aside.

In a small bowl, stir together the room temperature butter, brown sugar, and cinnamon until fully combined. It should resemble a paste consistency.

Spread the filling over the dough in an even layer, leaving a 1 inch border on all sides so it doesn’t leak out when baking. Starting on one side, roll the dough up using the parchment paper as a guide. It’s okay if the dough splits a little. Place in the freezer for 20 minutes.

Remove the log from the freezer and cut into even slices using a sharp knife. About 2/3 inch to almost an inch in thickness. I usually cut the log in half, and then keep cutting each portion in half until I’m left with about 16 cookies.

Place the cookies back in the freezer for another 30 minutes. Once there's about 5-7 minutes left, preheat the oven to 375° F. Line a baking sheet with parchment paper.

Bake 6 cookies at a time for 10-11 minutes or until edges are lightly golden brown. Set aside to cool completely before icing.

Add powdered sugar, heavy cream, and vanilla to a small bowl. Whisk until smooth. Drizzle over the cooled cookies.