Dough (15 min plus 1 hr): Mix flour, sugar, yeast, salt and cardamom. Add warm milk and egg and knead 5 minutes, then knead in the butter piece by piece for 8 minutes more, until smooth and springy. Cover and rise until doubled, about 1 hour.
Filling (3 min): Beat the butter, brown sugar, cinnamon and salt into a soft, spreadable paste.
Roll (10 min): Roll the dough to a 35 x 50 cm (14 x 20 in) rectangle and spread the filling right to the edges.
Shape (10 min): Roll up tightly from a long side. Cut into 16 slices, about 3 cm thick. Set them cut-side up in paper cups or on lined trays (for snails, lay them flat; for big Wednesday snails, roll the dough thinner and cut 8 wide slices).
Proof (40 min): Cover and proof 30 to 40 minutes until puffy. Heat the oven to 220C (425F).
Bake (10 to 12 min): Brush with beaten egg, scatter pearl sugar, and bake 10 to 12 minutes until deep golden. Cool a little under a towel to keep them soft.
Tips
Hot and short is the Swedish way: high heat keeps the buns soft inside.
For Icelandic-style sticky buns, brush with a glaze of melted butter, brown sugar and cocoa while warm.