In the bowl of a stand mixer fitted with the dough hook, whisk together the all-purpose flour, bread flour, granulated sugar, instant yeast, and salt. In a separate small bowl, whisk the warm milk and the egg together. Pour the wet ingredients into the dry ingredients and mix on low speed until a shaggy dough forms. Add the softened butter, one tablespoon at a time, until incorporated. Increase speed to medium and knead for 5-7 minutes, until the dough is smooth and pulls away from the sides of the bowl.

Form the dough into a ball and place it in a lightly oiled bowl, turning to coat. Cover the bowl with plastic wrap or a clean kitchen towel and let it rise in a warm, draft-free spot for 60-90 minutes, or until it has doubled in size.

Gently punch down the risen dough and turn it out onto a lightly floured surface. Roll it into a rectangle approximately 12x18 inches. Scatter the cubes of cold butter over two-thirds of the rectangle. Fold the unbuttered third of the dough over the middle third, then fold the remaining buttered third over the top, like a business letter. Roll this package out again into a 12x18-inch rectangle and repeat the letter fold one more time.

Wrap the folded dough tightly in plastic wrap and place it in the refrigerator to chill for at least 30 minutes. This step is crucial for creating flaky layers as it keeps the butter cold and allows the gluten to relax.

Once chilled, unwrap the dough and roll it out on a floured surface into a final 12x16-inch rectangle. In a small bowl, mix together the dark brown sugar, cinnamon, and pinch of salt for the filling. Brush the surface of the dough with a little melted butter or water, then sprinkle the cinnamon-sugar mixture evenly over the entire surface, gently pressing it down. Fold the rectangle in half lengthwise to create a 6x16-inch rectangle.

Using a pizza cutter or a sharp knife, cut the folded dough into 1-inch wide strips (about 16 total). Take one strip, hold both ends, and twist it several times in opposite directions. Place the finished twists on a parchment-lined baking sheet, leaving a couple of inches between each one.

Cover the baking sheets loosely with plastic wrap and let the twists rise for another 30-45 minutes, until slightly puffy. While they rise, preheat your oven to 400°F (200°C). Bake for 15-18 minutes, or until the twists are a deep golden brown and cooked through.

While the twists are baking, prepare the glaze. In a small bowl, whisk together the sifted powdered sugar, vanilla extract, and 2 tablespoons of milk. Add more milk, a tiny bit at a time, until you reach a smooth, pourable consistency. Let the baked twists cool on the baking sheet for 5-10 minutes before drizzling the glaze generously over them.