Stir together milk and yeast in a large bowl until the yeast dissolves.

Mix in the butter, eggs, 3½ cups flour, sugar, cardamom, and salt with a wooden spoon.

If the dough is very sticky, mix in up to ½ cup more flour.

Cover the bowl with plastic wrap and let the dough rise for 30 minutes.

Mix together butter, sugar, and cinnamon in a bowl until well combined.

Assemble and Bake Rolls:

Transfer the dough to a floured surface and knead until smooth, about 3 minutes.

Divide the dough in half.

Roll each half into an 8×10-inch rectangle that’s no more than ½ inch thick.

Spread each rectangle with half of the filling.

Stack one rectangle over the other, with the filling sides up.

Starting with a long edge, roll up the dough to form a long log.

Cut crosswise into 1-inch-thick slices.

Arrange the rolls 3 inches apart on 2 parchment paper-lined baking sheets, setting uneven end pieces cut sides up.

Let the rolls rise for 20 minutes.

Preheat the oven to 425°F.

Bake the rolls until they are golden brown, which usually takes about 10 to 12 minutes.

Stir together powdered sugar, milk, and vanilla in a small bowl.

Drizzle the icing over the warm rolls.

Enjoy your Danish Cinnamon Snails!