In the bowl of a stand mixer stir the sugar, milk and yeast. Let stand until foamy, about 10 minutes.
In another bowl mix together the flour, cardamom and salt. Add this and two of the eggs to the yeast mixture. Attach the dough hook and knead on setting 2 for until the dough looks shaggy. Add the butter and continue to knead until the dough starts to look shiny. If it is too soft to be kneaded in the machine dump it out onto a lightly floured surface and knead by hand.
Transfer to a lightly oiled bowl and cover, let rise until doubled (an hour or more).
Dump the risen dough onto a lightly floured surface and divide into three equal pieces. Roll each piece into a rope around 16” long. Lay the ropes next to each other and braid them together, tucking the ends under. Place on parchment paper on a baking sheet. Lay a towel over and let it rise and get puffy, about 45 minutes.
Preheat oven to 350F. In a small bowl beat the remaining egg with a little water, brush the bread with gently with the eggwash, sprinkle with the sliced almonds and demerara sugar. Bake until golden brown, about 35 minutes.