Beat eggs and sugar (reserved 1 Tbsp. Sugar for the yeast) in a large bowl.
Warm milk to 105°F to 115°F. Sprinkle yeast and a little sugar over the milk and let it "proof" for ~ 5 minutes. It should be bubbling.
Place flour and salt in a really large bowl. Add eggs and sugar mixture, yeast, vanilla, milk and melted margarine (mix food coloring in margarine if you want a slightly yellow bread and mix together with a large wooden spoon.
Turn out onto a board and knead until the dough is smooth. Place in a large, clean bowl, cover with a kitchen towel, and allow to rise for about an hour to an hour and a half, until doubled in size. (I like using a large metal bowl for this as it holds the heat in the best)
Turn out onto a wooden board and punch down and knead again briefly. Split in fourths (about 1-1/2 pounds each) and place all but one back in the bowl.
Break the first ball into 3 equal pieces and roll into long "logs" (about 12-15 inches). Line them up next to each other and press the ends on one side together. Braid the three pieces and finish by pressing the other ends together. Repeat with each ball of dough.
Place loaves on individual baking sheets, cover with a towel and let rise for an hour to an hour and a half.
Brush each loaf with a beaten egg and bake in a preheated 275°F oven for one hour.
Notes
Once cooled wrap each loaf tightly with plastic wrap. They will stay fresh in the freezer for a month or two.