How to Make It
Lightly flour a work surface.
Combine the milk and yeast in the bowl of a stand mixer and whisk well by hand. Add ¼ cup of the granulated sugar, the flour, and salt. Add the cubed butter and, using a dough hook, mix on low speed until a soft dough forms, 2 to 3 minutes. Transfer the dough to the work surface and finish kneading by hand until it forms a smooth, soft ball.
Line a baking sheet with parchment paper. Lightly dust it with flour and place the ball of dough on it. Cut two slits 1 inch deep into the ball in an X pattern. Wrap the baking sheet with plastic wrap and refrigerate overnight.
Put the room-temperature butter in the bowl of a stand mixer fitted with a paddle attachment and mix on low speed until smooth. Scrape the butter onto a piece of parchment or plastic wrap and shape into a 6 by 8-inch rectangle. Wrap in parchment paper or plastic wrap and refrigerate overnight.
The next day, remove the butter block from the refrigerator to soften for 15 for 20 minutes before starting to roll out the buns. It is important that the butter and the dough have similar consistencies.
Lightly flour a work surface.
Put the dough on the prepared work surface. Roll the dough into a 10-inch square. Unwrap the butter and place in the center of the dough. Starting with the left side, fold the dough over the butter, stretching it slightly if needed to reach the center of the butter; repeat with the other corners of the dough to completely enclose the butter block. Take your rolling pin and gently press down on the top. It is very important to seal in the butter completely.
Turn the dough 90 degrees. Roll the dough into a 12 by 10-inch rectangle. Brush off the excess flour. Take the left side of the dough and fold it into the center, then take the right side and fold it into the center to form a rectangle. This is the first tri-fold.
Roll the dough again into a 12 by 10-inch rectangle. Brush off the excess flour and fold the dough into thirds again. Put the dough back on the baking sheet and refrigerate for 30 minutes.
Lightly flour a work surface. Roll the dough with the sealed end to the left side, into a 12 by 10-inch rectangle. This time, fold the left side of the dough into the center. Fold the right side to meet the left edge in the center, then fold the left side over; this final turn is a bookfold. Rotate the dough 90 degrees. Roll the dough out into a 12 by 10-inch rectangle. Brush off excess flour. Fold the dough into thirds this time. Place on the prepared baking sheet. Wrap in plastic wrap and refrigerate for 3 hours.
Lightly flour a work surface. Place the chilled dough on the prepared work surface. Roll the dough to ¼-inch thickness and, using a pizza cutter, cut into ½-inch squares. Place the dough in a sealed container and refrigerate for at least 4 hours, or up to overnight. Squares can be frozen for 4 days and thawed in the refrigerator the night before you plan to prepare the buns.
In a small bowl, combine the remaining ½ cup granulated sugar, cinnamon, and cardamom. In a large bowl, whisk the egg and toss the cubed dough into the egg to break it apart and coat each cube. Sprinkle the spiced sugar in and toss to coat completely.
Spray a standard muffin pan with nonstick cooking spray, making sure to spray the portion of the pan between the cups, because the buns will expand. Place a standard muffin paper liner in each.
Fill each paper liner with sugared dough, about 12 cubes per muffin. Press down firmly. Cover the entire pan with plastic wrap and let rise at room temperature for 11⁄2 to 2 hours. The dough will be soft and puffy when touched.
Preheat the oven to 350°F.
Place the muffin pan on a baking sheet and bake until the buns are puffed and golden in color, 35 minutes. Cool completely in the pan before glazing.
To make the glaze, sift the confectioners’ sugar into a bowl. Whisk in orange juice, orange blossom water, and orange zest until the glaze has a smooth, thick consistency. Place a generous spoonful on each morning bun. These buns are best served the day they are made.