In a large bowl, dissolve yeast in warm water. Add the milk, sugar, butter, eggs and 1-3/4 cups flour; beat until smooth. Combine the cardamom, salt and remaining flour; gradually add to dough (dough may seem sticky, but do not add more flour).
Turn onto a lightly 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 hour.
Punch dough down. Turn onto a lightly floured surface; divide into thirds. Shape each portion into a 20-in. rope. Place three ropes on a greased baking sheet and braid; pinch ends to seal and tuck under. Cover and let rise until doubled, about 1 hour.
Bake at 375° for 25-30 minutes or until golden brown. Remove from pan to a wire rack. Brush with melted butter. Cool.
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