Warm the milk until just hot to the touch, then stir in a pinch of the sugar and the yeast. Let stand until foamy, 5–10 minutes.
Whisk in the melted butter, egg, remaining sugar, salt, and cardamom.
Add flour gradually and mix until a soft dough forms. Knead on a lightly floured surface until smooth and elastic, 8–10 minutes.
Grease a bowl, place the dough inside, and cover. Let rise in a warm spot until doubled, about 60–75 minutes.
Stir together brown sugar and cinnamon for the filling. Keep the softened butter, raisins, and almonds ready.
Punch down the dough and roll into a 10×18-inch rectangle on a floured surface.
Spread the softened butter over the dough. Sprinkle evenly with the cinnamon sugar, then scatter raisins and almonds over the top.
Roll up tightly from a long edge to form a log, pinching the seam to seal.
Transfer the log to a parchment-lined sheet and shape into a ring, sealing the ends together.
Snip slits around the ring every 1–1½ inches, cutting two-thirds of the way through. Gently twist each slice slightly outward to fan.
Cover lightly and let rise until puffy, 25–35 minutes. Meanwhile, heat the oven to 350°F.
Bake until deep golden and set, 25–30 minutes. Cool on the pan for 15 minutes.
Whisk powdered sugar, vanilla, and milk until smooth. Drizzle over the warm ring and let set a few minutes before slicing.