Put the flour into a bowl and make a small well in the middle. In a small bowl or glass measuring cup, dissolve the yeast in the milk, and set aside for 15 minutes, until the mixture is foaming.
Pour the yeast mixture into the well, along with 1/3 cup sugar and two egg yolks. Add a pinch of salt and 1/3 cup softened butter. Stir to combine, or use your hands to mix, adding the flour gradually to the liquid mixture in the center.
Knead together on a lightly floured surface until a smooth dough is formed, about 10 minutes. Cover and let rise for around 45 minutes in a warm place.
Knead the dough again, then roll out on a lightly floured surface with a floured rolling pin to form a rectangle approximately 12×27.5 inches (30×70 cm) in size.
In a small bowl, combine the cinnamon with the remaining sugar. Cut the cold butter into small pieces or grate with a cheese grater. Spread the butter pieces and the sugar-cinnamon mixture evenly on the dough.
Roll up the dough from the long side and gently press together to seal the end. Cut the roll into 2-inch-thick slices (5 cm).
Take the end of a spoon and press into the middle of each slice so that the layers become visible, comparable to a squeezed snail shell.
Put the buns onto baking trays lined with parchment paper, cover with a clean kitchen towel, and let rise for 15 minutes.
Meanwhile, preheat the oven to 180°C/360°F (convection oven 160°C/320°F).
Whisk the remaining egg yolk together with some milk to make a wash, and brush it onto the pastry.
Bake for 15 minutes, or until golden. Cool on wire racks.