In a bowl, dissolve yeast in warm water. Add warm milk, sugar, butter, 2 eggs, cardamom, salt and 6 cups flour; beat until smooth. Stir in enough remaining flour to form a soft dough.
Turn onto a floured surface; knead until smooth and elastic, about 6-8 minutes. Place in a greased bowl, turning once to grease top. Cover and let rise in a warm place until doubled, about 1-1/4 hours.
Punch dough down; cover and let rest for 10 minutes. Divide into fourths. Divide each portion into thirds; shape each into a 12-in. rope. Place three ropes on a greased baking sheet and braid; pinch ends to seal and tuck under. Repeat with remaining dough. Cover and let rise in a warm place until nearly doubled, about 45 minutes.
Preheat oven to 375°. Beat remaining egg; brush over loaves. Sprinkle with sugar. Bake until golden brown, 20-25 minutes. Remove from pans to wire racks.