Add the milk, instant yeast, unsalted butter, and egg to the bowl of a stand mixer, followed by the sugar, bread flour, all-purpose flour, and salt.
Using the dough hook attachment, mix all the ingredients together until a dough forms. Then, turn the speed to 4 and knead for about 10 minutes.
Once the dough is smooth, stop kneading and let it proof in a large, greased bowl for 1 hour. After an hour, transfer the dough to a floured surface and knock out all the air. Roll the dough into a round shape, about 16 inches in diameter.
Use a pizza cutter to cut the dough into 16 triangles, and cut 1/2 stick of cold butter into 16 small cubes. Preheat the oven to 350°F (176°C).
Place a butter cube at the bottom of each dough triangle.
Tug and roll the dough up to form a crescent roll shape.
Pinch the end to secure it. Transfer each butter roll to a baking sheet lined with parchment paper, placing the top side facing down. Let them proof for a second time for 1 1/2 hours.
Gently brush the butter rolls with melted butter and sprinkle the tops with sea salt flakes. Bake in the oven for 10 to 15 minutes, or until the surface of the rolls is light golden brown.
Remove from the oven and serve warm with butter or any fruit preserves or jam.