In a large bowl, whisk together flour, sugar, yeast, and salt.

Add lukewarm milk and softened butter. Mix until a shaggy dough forms.

Turn the dough out onto a lightly floured surface and knead for 8-10 minutes until smooth and elastic. Place in a greased bowl, cover, and let rise in a warm place for 1-2 hours, or until doubled in size.

Punch down the dough. Roll it out into a large rectangle (about 12x18 inches).

Scatter the cold butter cubes evenly over two-thirds of the dough rectangle. Fold the unbuttered third over the middle third, then fold the remaining buttered third over that, like folding a letter. You should have three layers of dough with butter in between.

Rotate the dough 90 degrees and roll it out again into a long rectangle. Fold it into thirds again. Repeat this process 2 more times, ensuring you chill the dough for 30 minutes in between each set of folds. This creates the flaky layers.

Roll the final dough into a rectangle (about 10x16 inches). Cut it into 12 equal strips.

Roll each strip up loosely, starting from one end, to form a spiral. Place each rolled cruffin into a greased muffin tin.

Cover the muffin tin and let the cruffins rise for another 30-60 minutes.

Preheat oven to 375°F (190°C). Bake for 18-22 minutes, or until golden brown and puffed.

While the cruffins are cooling slightly, whisk together powdered sugar, milk, and vanilla extract until smooth. Drizzle over the warm cruffins.