Add 2 cups milk and sugar to a small saucepan over medium-low heat.
Whisk until combined and add butter.
When the butter has melted, remove from the heat and let it cool down to a warm bath temperature before stirring-in yeast. Too cool and the yeast will not activate, and too hot and the yeast will die. I use a thermometer and like it to be in the 100° to 118° range. You will know that your yeast has activated when bubbles begin to form.
While the yeast is cooling, add 2 cups flour, salt, cardamom, and one egg to the bowl of a stand mixer with the dough hook attached.
Pour the milk mixture into the bowl and stir until combined.
Put in 3 more cups of flour.
Stir until completely incorporated.
Add the remaining cup of flour, a little at a time.
Stop when the dough forms a ball and is no longer sticky to the touch.
Transfer the dough to a large, lightly oiled bowl. Cover with plastic wrap. I like to go an extra step and put the bowl inside of an extra large Ziploc bag. It creates a draft-free rising environment. Let rise until doubled, about one hour.
Turn the dough out onto a well-floured board. Punch the dough down, knead by hand for one to two minutes, then let the dough rest for 10 minutes. Preheat oven to 375°.
Divide the dough into 6 equal pieces. (I weigh the dough using a kitchen scale and then divide the weight by six to get the correct amount of dough.)
Roll the pieces into a skinny rope about 15 inches long.
Line up three pieces of dough and pinch the top together. Braid the three pieces into a loaf. Pinch the bottom and tuck underneath. Repeat with the other three ropes.
Transfer to a parchment-lined baking sheet and rise for another 30 minutes. Make an egg wash by whisking the remaining egg and one tablespoon milk. Brush the sides and top with wash and sprinkle pear sugar all over.
Bake the loaves for 20 minutes, or until golden brown. Let cool before slicing.