Prepare the Tangzhong: In a medium saucepan, combine 3 tablespoons of all-purpose flour and 1/2 cup of water. Whisk continuously over medium heat for about 4-5 minutes, until thickened. Let it cool to room temperature.

Mix Dry Ingredients: In a stand mixer, combine 2 cups of all-purpose flour, 1/4 cup of granulated sugar, 1 tablespoon of instant yeast, and 1/2 teaspoon of fine sea salt. Mix on low speed for about 30 seconds.

Combine Wet Ingredients: Add 1/2 cup of heavy cream, 1/4 cup of whole milk, 1 room temperature egg, and the cooled tangzhong to the dry ingredients. Mix on medium speed until a soft dough forms.

Knead the Dough: Gradually add 2 tablespoons of unsalted butter, incorporating fully before adding more. Continue mixing for about 8-10 minutes until the dough is smooth and elastic.

Rest the Dough: Place the kneaded dough in a greased bowl, cover with a damp cloth, and let it rise in a warm spot for 30 minutes.

Make Cookie Dough Filling: Cream together 1/4 cup of unsalted butter, 1/4 cup of light brown sugar, and 1/4 cup of granulated sugar until light and fluffy. Add 1 room temperature egg and 1 teaspoon of vanilla extract. Mix well.

Roll Out the Dough: On a floured surface, roll the rested dough into a 15x21-inch rectangle, about 1/4 inch thick.

Fill and Roll: Spread the cookie dough filling evenly across the dough, leaving a small border. Starting from an edge, tightly roll the dough into a log and pinch the edges to seal.

Second Rise: Cut the rolled dough into 12 equal pieces and place in a greased baking dish. Cover and let rise for about 1 hour.

Bake: Preheat oven to 350°F (175°C) and bake for 30-40 minutes, or until golden brown and cooked through.

Prepare Frosting: Blend 2 tablespoons of unsalted butter, 4 ounces of cream cheese, 1 cup of powdered sugar, 2 tablespoons of heavy cream, and 1 teaspoon of vanilla extract until smooth.

Top and Serve: Once baked, cool for 10 minutes and drizzle the glaze over the warm rolls before serving.