Start by heating 60g of the butter and all of the milk together in the microwave until the butter is melted and the milk is warm (but not scalding hot or boiling).
In a big bowl: whisk together 400 grams of the flour (reserve the extra 50 for later, if needed), 50 grams of the sugar, and the salt.
In the standing mixer, with the dough hook on: Add the warm milk/butter mixture and sprinkle the yeast on top. Mix with a fork, then let sit for a couple of minutes until the yeast has dissolved.
Add the flour mixture and the egg, and knead on low speed until the dough forms a ball. If the dough is very sticky, add a bit of the 50 grams of the reserved flour, as necessary. Note: the dough will be a bit sticky even if you add all 50 grams of the extra flour, but that's ok! Knead for 5 minutes, then shape the dough into a ball, place it in an oiled bowl, cover it with plastic wrap or a kitchen towel, and leave it in a warm place to rise (until ideally doubled in size, if not, for at least 15 minutes).Note: how long this takes depends on how warm it is in your home!
While you're waiting for the dough to rise, mix the cinnamon, brown sugar, cardamom and remaining white sugar together in a small bowl. This is the filling for the cinnamon rolls.
It's time to roll out the dough! Roll it out on a floured surface, into a rectangle shape. You're aiming for something that's a bit bigger than an A4 sheet of paper. Spread the rest of the softened butter gently all over the dough, either using a pastry brush or your fingers, then sprinkle the cinnamon/cardamom/sugar mixture on top.
Roll it up! Starting from the longer side of the rectangle, tightly roll up the cinnamon roll until you've reached the end, and try to pinch the edges shut so that it doesn't unroll too much.
Slice the cinnamon rolls. Using a piece of string placed under the cinnamon roll, pull upwards and then criss-cross your hands so that the cinnamon roll slices off perfectly. If you don't have a piece of string, you can simply slice the rolls with a sharp knife, but they will get a bit squashed like this. You should end up with 11 or 12 cinnamon rolls: I recommend starting your first slice from the middle of the dough so that you can end up with relatively even rolls.
Place the cinnamon rolls in a baking dish (any high-rimmed tray, cake or tart dish works fine), nestling them up nicely next to each other. Cover the dish with a kitchen towel and let the cinnamon rolls rise again, for at least 30 minutes.
Preheat the oven to 180° C.
Remove the kitchen towel and bake the cinnamon rolls for 15-20 minutes (or until they're nicely puffed up and golden brown), and then let them cool for about 5 minutes before sneaking one to check if they're good (they are!) and burning the roof of your mouth (you will!).
While they cool, make the icing.