Preheat oven to 350 degrees.
Mix the Wet Ingredients: Place butter and sugar in a large bowl of a stand mixer, or using a handheld mixer, beat on medium speed until creamy, about 1-2 minutes. Add egg and vanilla and continue beating for another 30 seconds.
1 cup butter, 1 cup granulated sugar, 1 egg, 1 tsp. vanilla
Whisk the Dry: In a separate large bowl, whisk together flour, ½ teaspoon salt, baking powder, and ½ teaspoon of cinnamon.
3 cups all purpose flour, ½ tsp. salt, 1 ½ tsp. baking powder, ½ tsp. cinnamon
Add Dry to Wet: Slowly add dry ingredients to the wet ingredients, mixing on low-speed after each addition. Once dough is thick and thoroughly mixed, refrigerate for 30 minutes, and no longer than 1 hour.
Prepare Filling Ingredients: Melt butter in a small bowl and set aside. Whisk together ⅓ cup brown sugar, ⅓ cup granulated sugar and 1 teaspoon cinnamon in a separate small bowl.
⅓ cup brown sugar, ⅓ cup granulated sugar, 3 Tbsp. butter, 1 tsp. cinnamon
Roll out and Fill: Place a 20 to 24-inch long sheet of wax paper onto a flat surface. Add the refrigerated cookie dough in the middle of that paper and roll out into a 16” x 8” rectangle. If not a perfect rectangular shape, cut and trim the edges and keep rolling the dough until it is. Using a pastry brush, spread half of the melted butter over the dough and then sprinkle half of the cinnamon sugar over the butter.
Shape Dough into a Log: Starting from the longer side, roll dough into a hot dog shape or log, reinforcing the shape as you go to ensure it is tight. (The dough may crack slightly- that's totally ok! Just smooth out the cracks and keep rolling.) You should end up with a 16"-long log. Refrigerate the dough for another 30 minutes before slicing.
Slice and Bake: Slice the cooking dough into 16 pieces. Place the slices onto a parchment paper-lined cookie sheet at least 2-inches apart. Bake in the preheated oven for 10-12 minutes. Repeat the above steps with the other half of the dough. Wait for cookies to cool completely before finishing with the cream cheese glaze.
Make the Glaze: While the cookies are baking, add cream cheese, butter, powdered sugar, and vanilla to a medium-sized bowl and beat on medium-speed with an electric hand mixer until smooth and creamy. Pour in milk, 1 tablespoon at a time, and beat until your desired consistency is reached.
1 ½ Tbsp. cream cheese, 1 Tbsp. butter, 1 ¾ cup powdered sugar, ½ tsp. vanilla, 1-2 Tbsp. milk
Ice the Cookies: Place cream cheese glaze in a Ziploc bag and cut off a small corner of the bag to create a piping bag or add the glaze to a piping bag fitted with a small round tip. Drizzle the glaze over cooled cookies.