In a small saucepan, combine the milk and sugar; whisk until the sugar is dissolved. Add the butter, and heat over medium low, stirring gently, until the butter is melted. Remove from the heat.

Allow the milk mixture to cool to the temperature of a warm bath (not hot!), and stir in the yeast. Allow the mixture to sit for 5 minutes to make sure the yeast is active and alive. You should see bubbles on the surface (don't be alarmed if it's not super foamy), and the mixture should grow in volume.

When you are certain the yeast is working, in a large bowl with a wooden spoon or in the bowl of a stand mixer fitted with the dough hook attachment, add the milk mixture. Add 2 cups of the flour, and the salt, cardamom, and 1 of the egg. Mix until combined.

Add 3 more cups of the flour and stir until it is completely incorporated. Add the remaining 1 cup of flour a little at a time until the dough forms a ball and is no longer super sticky when lightly touched with your finger. You might not use the entire cup of flour.

Transfer the dough to a large, lightly oiled bowl, cover it with plastic wrap, and let it rise in a warm spot until doubled in size, about 1 hour.

Punch down the dough, knead by and for 1 to 2 minutes on a well-floured surface, and let rest for 10 minutes.

Divide the dough into six equal portions. Roll each portion into a skinny rope about 15 inches long. Line up three dough ropes side by side on the counter in front of you. Pinch one end of the rope together, then gently braid the three ropes into a loaf. When you reach the end, pinch the remaining dough together and tuck it under the loaf slightly. Repeat with the other three dough ropes to make a second loaf.

Place each loaf on a parchment-lined baking sheet, and let it rise for 30 minutes.

Preheat the oven to 375 degrees F.

To make an egg wash, in a small bowl, whisk the remaining 1 egg and the milk together. Brush the top and sides of both braided loaves with the egg wash, then sprinkle each loaf with 1 tablespoon pearl sugar.

Bake the loaves until browned on top, about 20 minutes. Remove from the oven and allow them to cool before slicing.