Add all ingredients except the egg and toppings to a large mixing bowl and stir together with a sturdy wooden spoon until you form a shaggy but cohesive dough. Let the dough rest for 30 minutes, covered with a clean towel. Turn out onto a lightly floured counter top and knead until smooth and elastic, about 10 minutes. Transfer dough to a clean bowl, cover with a damp towel and let rise in a warm, draft-free place until doubled in size, about 2 hours.
!To Mix Dough By Stand Mixer:
Add all ingredients except the egg and toppings to the work bowl of your stand mixer fitted with the dough hook. Turn mixer onto the lowest setting and mix until a shiny, elastic dough forms. Remove the bowl from the mixer, cover the bowl with a damp towel and let rise in a warm, draft-free place until doubled in size, about 2 hours.
!To Mix Dough By Bread Machine:
Add all ingredients except the egg and toppings to the pan of your bread machine that has been fitted with the dough paddle(s). Set the bread machine on the dough setting and press start. When the cycle is completed, proceed with shaping...
!To Shape the Dough:
Turn the dough out onto a clean surface and form into a neat mass. Divide the dough in half, then divide each half into 3 pieces. Cover three of the pieces with a towel while working with the other three.
Pat one piece into a rough oval. Use the side of your hand to press an indentation along the length of the dough piece. Fold the dough together along the length of the indentation and roll lightly with the hands to form a thick rope between 12 and 14 inches long. Repeat with the other two pieces so that you have 3 ropes of roughly equal length. Line them up in parallel with the ends facing you.
!To Braid the Dough:
Gently grasp the end of the rope on the far left. Lift it to about the center, leaving the far end on the counter, cross it over the rope nearest to it and lay it down. Now grasp the end of the piece on the far right and lift it to about the center, leaving its far end on the counter, cross it over the (now) center rope (which is the first one you moved) and lay it down. This is the manoeuver you will repeat - far left over center, far right over center, and so on- until you have ends too short to continue. At that point, pinch the ends together and tuck under the braid. Now go back to the center of the loaf and finish braiding the loaf toward the top. When you reach the ends, pinch together and tuck under. Cover the loaf lightly and let rise in a warm place until puffy in appearance and about doubled in size.
Preheat oven to 400°F. Whisk the egg until very loose. Paint generously onto the risen bread braids and sprinkle the braids with desired toppings.
Bake for 18-26 minutes or until your preferred shade of golden to deep brown and firm on top. Turn the oven off, prop the door open a little (two inches, if you can make your door behave) and let cool for at least an hour. Or tear into the loaves with your teeth. I won't tell.