Sweden isn't much of a doughnut country. Sure, you can find some at cafes or even the grocery store but they honestly stick out as misfits compared to all of the traditional pastries and treats.
Perhaps these traditional buns are why.
Whatever the reason, they are tasty and certainly worth the (fair amount of) hassle.
You'll need:

about 2 1/2 cups of flour (you'll need to judge the exact amount by the dough's consistancy), 3/4 cup whole milk, an egg, 5 tablespoons butter, 25 grams cake yeast, 3 tablespoons sugar. (Not pictured, 1 tsp salt)
If you've got a powerful mixer you can really just dump all of this in the bowl and mix for about 20 minutes (adding the salt after 10 minutes). Otherwise, melt the butter and heat the milk to 97 degrees F. Dissolve the sugar into the butter and milk. Add this mixture to a mixing bowl and dissolve the yeast in it. Dump in your flour and egg, mix to combine and knead until smooth and elastic.



After kneading, let the dough rest and rise until doubled in volume (about an hour).
Next, assemble your fillings and dump out the dough onto a prepared work surface.

I went ahead and did two fillings: applesauce and vanilla creme. The applesauce was made with ripe Antonopka (ripe in October, good eating, excellent baking and applesauce) apples from our tree (plus sugar and cinammon). You want an assertive and thick applesauce for these buns. I've documented making vanilla creme
elsewhere.
Roll the dough out to roughly 1/4 inch thickness and stamp out 3.5 inch rounds.

Spoon about 1 tablespoon of filling onto each round. It's really tempting to spoon out too much. However, this will only cause headaches later so resist! Besides, there are worse thing in life than leftover vanilla creme...

Carefully fold the edges of each round up and around the filling. You can't get any of the filling on the edge or it simply won't seal. Pinch all of the edges together and seal as well as possible (although be careful to not strech the dough too thin on the filling side...). Something like this:




Place the filled and seal buns on parchment-lined baking sheets and let rest...

... and rise until nearly doubled in size (about 30 minutes):

Bake in a very hot (500 degree) oven for about 10 minutes. Keep an eye on them, though. These came out in the nick of time:

While still warm, brush the buns with melted butter and roll in sugar.

Do yourself a favor and eat a few while still warm!
The vanilla creme:

The applesauce: