In a small bowl, whisk the milk and yeast. Whisk in two of the eggs and vanilla and set aside.

In the bowl of a stand mixer fitted with the paddle attachment, mix the flour, 1/4 c of sugar and the salt. Add the cold butter cubes and mix on low speed until they are broken down to the size of small peas, about 1-2 minutes. With mixer running, drizzle in the milk mixture and mix just until a dough forms.

Lightly flour a work surface and turn out the dough onto it. Knead gently to form a ball, then flatten it into a disk about 1″ thick. Wrap tightly in plastic wrap and refrigerate until firm, about 6 hours or overnight. (I did overnight.)

About 2.5 hours before you plan to serve the buns, take the dough from the fridge. Line two baking sheets with parchment. In a 2 c measuring cup, combine the remaining sugars, cardamom and cinnamon. Mix well.

In a small bowl, beat the remaining egg with a splash of water and set it aside.

Lightly flour a clean work surface and rolling pin and roll out the dough into a 12×16″ rectangle. With the short side facing you, use a spatula or the back of a spoon to spread the softened butter in an even layer over the dough, leaving a 1″ border along the top and bottom edges of the rectangle. (If the butter is cold, I place it in the microwave in its paper wrapper and heat it for 10 seconds.) Sprinkle the sugar mixture over the butter, then brush the bare borders with the remaining beaten egg, reserving the rest for later. Fold the dough in half so the egg washed borders meet, then cut it perpendicular to the fold in 12 even strips. Press gently together.

Working one at a time, left each of the strips by their two short ends, and twist in opposite directions while pulling and stretching slightly to make a loose twist. Coil the strip around one of its own ends to make a circular bun, then tuck the outermost end beneath the dough.

Transfer to the baking sheet, leaving three inches between each bun. (At this point I refrigerated my buns, covered them and kept them overnight to bake before brunch. I then took them out to rise at room temperature for about 2 -3 hours before baking.) Cover with plastic wrap and set aside until the buns are puffed and soft, about 1.5 hours.

Preheat the oven to 400 and place two racks near the center with at least 5″ between them. Brush the surface of each bun with egg wash, then bake, rotating the sheets halfway through, until golden brown, 20-25 minutes. Remove and sprinkle with the leftover sugar that will fall from your coils. Let cool slightly before serving.