Whisk the sugar, yeast and 1 cup of the warm water in a medium bowl. Set aside to bloom.
Add the flour to the bowl of a stand mixer fitted with the hook attachment. Make a well in the center of the flour and bury the salt in the well. Add the canola oil, whole egg, remaining 1 1/3 cups warm water and the bloomed yeast, making sure no sediment is left behind. Mix on low speed for 30 seconds, increase to medium speed for 30 seconds and then increase to high speed for 3 minutes, mixing until the dough appears smooth.
Spray a large bowl with nonstick cooking spray and transfer the dough to the bowl. Cover with a damp towel or plastic wrap and set in a warm area to proof until doubled in size, about 1 hour.
Turn the dough out onto a lightly floured surface. Split the dough into 3 loaves. Divide each loaf into the desired number of braid strands (3, 4 or 6) and roll each strand to elongate. Braid the strands to a long loaf or a round shape and place on a baking sheet lined with parchment paper.
Whisk together the egg yolk with a pinch of salt and a pinch of sugar. Brush this egg wash over the shaped loaves and top with 1 tablespoon zaatar per loaf, if using. Let the loaves rise in a warm place until doubled in size, about 30 minutes.
Preheat the oven to 350 degrees F.
Bake until lightly golden, 30 to 35 minutes. Transfer to a rack to cool.
To freeze, cool completely before transferring to a ziptop bag.