1.In a bowl warm milk in the microwave until warm to the touch. Add yeast and mix well then set aside.
2.In the bowl of an electric mixture with dough hook attached add bread flour, sugar, cardamom, and salt. Turn the machine on briefly to mix the dry ingredients.
3.Pour in the milk, 1 egg, and 4 tablespoons butter (57 grams). Mix on low speed 1 until the dough comes together, then increase to medium speed (speed 2) and continue kneading for 8 minutes. The dough should be smooth and elastic.
4.Scrape the dough inside the bowl and turn it around then cover with plastic wrap.Set it in a warm spot to rise until roughly doubled in size, about 1 1/2 hours.
5.Meanwhile, in a medium bowl add 4 tablespoons butter (57 grams), brown sugar, cinnamon, and flour. Using a spoon mix well until a paste forms then set aside.
6.Line a large baking sheet with parchment paper. Set aside. Dust a work surface lightly with flour. Transfer the dough onto the floured surface and sprinkle some more flour on top. Use a rolling pin, roll the dough into a rectangle of about 15 inches by 12 inches, with the long side parallel to the edge of your work surface.
7.Scoop the filling onto the dough and use a spatula to spread the filling into a thin, even layer over the entire surface. Starting with the edge nearest you, roll up the dough to form a 15-inch log, ending seam-side down. Use a sharp knife to cut the log into 12 triangular-shaped pieces, roughly 2 inches on the wide end and 1 inch on the narrow end.
8.Transfer the buns to the baking sheet, spacing them at least 2 inches apart. Rotate the buns so the narrow end faces up, reaching a peak. Use your finger to press into the center of each bun to fan out the spiraled edges. Cover with plastic wrap and leave in a warm spot to rise for 1 1/2 hours, or until they’re slightly puffy and almost doubled in size.
9.Preheat the oven to 400°F. In a small bowl, beat an egg with the water. Gently brush each bun with the egg wash and top with some pearl sugar. Bake the buns for 15 minutes or until golden brown.
10.Take the buns out of the oven and let it sit for 10 minutes. Use a spatula to transfer the buns to a cooling rack. Serve warm.