Add the warm water to the bowl of a stand mixer with the dough hook attached.  Add the yeast and 1 teaspoon of sugar.  Stir briefly and allow to blossom for 5 minutes.

Add the remaining 1/2 cup sugar, honey, butter, 3 eggs, salt and 4 1/2 cups flour to the bowl.  Starting on the slowest setting, mix with the dough hook until the flour is mostly incorporated.  Increase the speed to medium and mix for 5 minutes until the dough is smooth, but not completely dry.  Add more flour if needed to make a soft craggy ball.  Turn the dough out onto a lightly floured surface and knead by hand for 5 turns.  Place the dough in a lightly oiled bowl and turn to coat all sides.  Cover with a damp towel and allow to rise in a warm draft free area for 2 hours, or until doubled in size.

Punch the dough down and turn out onto a lightly floured surface.  Divide the dough into 3 equal pieces.  Using your hands, roll out each piece to a 14 inch rope.  Pinch the three rope ends together and braid loosely.  Pinch the other ends together and place on a parchment lined baking sheet.  Cover with a clean kitchen towel and let rise for another 45 minutes in a warm draft free place.

Preheat the oven to 350 degrees F.  Using a pastry brush, brush the beaten egg over the entire surface of the dough.  Bake for 30-35 minutes until golden brown.  Remove from the oven and allow to cool on the baking sheet for 10 minutes before removing to a wire rack to cool completely.