Heat milk until it's lukewarm and add it to a large mixing bowl. Stir in the yeast until dissolved.
Add the sugar, cardamom, and about 2/3 of the flour.
Mix the dough together either by hand or in a mixer with a dough hook and add the softened butter. Then slowly add the rest of the flour. You might need a bit more or less flour to form dough that isn't too sticky to knead. When the dough forms a nice ball continue to knead the dough for about ten minutes.
Cover and let rise until doubled in size (about one hour).
Vanilla Custard
Heat the milk and half of the sugar in a saucepan. Split open the vanilla pod with a knife and carefully scrape out the seeds and add them to the milk.
Mix together the rest of the sugar and the corn starch in a bowl. Add the egg yolks and whisk together until smooth.
Once the milk mixture starts to bubble pour about half of it into the bowl with the egg mixture, whisking quickly the entire time. Then return the saucepan to the heat and pour the egg and milk mixture from the bowl back into the saucepan, whisking the whole time. Let the custard cook for 2 minutes, whisking the entire time. By the end it should be quite thick and harder to whisk.
After 2 minutes remove the custard from the heat and pour into a clean bowl. Cover with plastic wrap, placing it directly touching the top of the custard. Let the custard cool while the dough finishes rising.
Almond filling
Run the almonds and sugar in a food processor for several minutes, until getting the consistency of soft marzipan. It should hold shape when you press it together. Add the milk (or egg whites) and pulse a few more times until incorporated.
Assembly
Divide the dough into 12 equal sections and roll each into a ball.
Use a rolling pin to roll out each bun into a circle about 7 inches (18 cm) in diameter). Add about a tablespoon of the almond filling to the center of the dough circle and fold the top top and bottom edges together and then the left and right edges, to make a square (see video).
Repeat with the rest of the buns and then let them rise again for about 30 minutes.
Preheat oven to 395°F (200°C).
Use a spoon or piping bag to add a generous portion of vanilla custard to the center of each bun (you can press down the center a bit to make more space for the custard).
Whisk the egg and salt together and brush each bun. Sprinkle with chopped almonds.
Bake for 15 - 20 minutes until the tops and bottoms of the buns are golden. Be careful not to over bake.
Once the buns have cooled, mix the powdered sugar and water (or egg white) and add it to a small plastic bag. Cut the tip off one corner and pipe the icing across the buns. Enjoy!