1.Heat 4 tablespoons butter in the microwave until it melts completely. Once the melted butter is slightly cooled, add 2 teaspoons milk, 1 egg yolk, vanilla, and 2/3 cup sugar. Mix with a spatula until smooth. Combine 1 cup flour, baking powder, and baking soda in another small bowl. Mix well then transfer to the bowl with the wet ingredients. Mix with a spoon until a dough forms. Use your hands to press the crumbs together into a thick dough log. Transfer the dough to plastic wrap and wrap the dough. Shaping the wrapped dough, so it forms a thick cylindrical log, about 2” in diameter. Place in the fridge to chill for 3 hours or overnight.
2.Add 3/4 cup milk into a small bowl and warm in the microwave for 30 seconds. Pour it into the bowl of a standing mixer. Add 1/3 cup sugar and yeast. Stir it slightly and let it sit for 5 minutes. Add the heavy cream, egg, bread flour, 1 3/4 cup flour, and 1 teaspoon salt into the bowl. Using a dough hook mix at setting 2 for 2 minutes. Add 3 1/2 tablespoons butter to the dough. Smear the butter into the dough. Turn the mixer to setting 6 and knead for 14 minutes, until the dough is smooth and stretchable.
3.Form the dough into a tight ball by pulling its sides to the bottom, then place back in the mixing bowl. Cover the top with plastic wrap and place it in a warm area. Allow to rise until double in size, for 1 hour.
4.Line a large baking sheet with parchment paper. Punch the dough softly and place onto a work surface and knead a few times. Cut the dough in half, then halve it again into four pieces, and cut each piece into four even pieces, so you get 16 pieces in total.
5.Form each dough piece into a tight ball by pulling its sides to the bottom. Roll gently with the palm of your hands to form a ball. Place the dough ball onto the lined baking sheet. Repeat with the rest of the dough balls. Cover the dough ball with plastic wrap and place in a warm spot to let rise for another 45 minutes, until double in size.
6.Combine 2 egg yolks, 2 teaspoon milk, and 1/2 teaspoon sugar in a small bowl. Whisk together until everything is combined. Cover and place in the fridge.
7.Grab the topping from the fridge and unwrap. Score marks on the dough so you can slice the log into 16 even pieces, then slice accordingly. Place topping piece between two pieces of plastic wrap. Flatten dough with rolling pin without cracking it, until it forms a round disk that is about 2.5” in diameter and 1/4” thick. Place the rolled topping disks stacked together by placing parchment paper between each piece of dough. Cover with plastic wrap until you’re ready to assemble the buns.
8.Preheat the oven to 350° F. Remove the plastic wrap from buns. Gently place the topping dough disks onto the bread dough rolls. Brush all the buns with egg wash. Bake for 15 to 17 minutes, until the top is golden yellow and the bottom is slightly browned. Let the buns rest in the pan for 5 minutes, then transfer them onto a cooling rack. Serve warm or at room temperature.