In large bowl, mix 1 cup flour, sugar, yeast and salt.  Heat water, 1/2 cup milk, and butter until butter melts.  Add to flour mixture and mix well.  Add egg and 1 cup of flour to mixture and mix well.  Gradually add remaining flour until dough is stiff.  Knead dough for 5 minutes (add flour as needed).  Place in large bowl and cover with a towel.  Place in warm area until doubled size (about 1-1/2 hours).  Meanwhile, mix brown sugar, butter and cinnamon; set aside.  Place dough on floured board and knead.  Divide dough in half and roll out 1/2 into oblong rectangle shape.  Spread 1/2 of cinnamon mixture on dough and roll dough to make a thin loaf shape.  Repeat with remaining dough and cinnamon mixture.  Wrap the 2 loaves together to form one braided loaf.  Pinch the ends together to have the loaf form an oval.  Cover with wax paper and a towel and place in a warm area to let rise, about 1-2 hours.  Bake in oven at 375 degrees for 25 minutes.  While cake is baking, make colored sugar for topping by mixing each of the separated 1/4 cup granulated sugars with food dye to make green, purple and yellow sugar; set aside.  Prepare glaze by mixing powdered sugar, vanilla and milk; set aside.  When cake is cool, pour glaze over cake.  Sprinkle with colored sugars.