Dissolve yeast and 1/3 cup sugar in 2 cups warm water in a large bowl. Let stand until a creamy layer forms on top, about 5 minutes. Stir in 3 cups flour to make a loose sponge.

Beat 1 cup sugar, 1/2 cup vegetable oil, 4 eggs, and 1 tablespoon salt together in a separate bowl. Stir into yeast-flour sponge until well combined. Continue mixing in flour, 1 cup at a time, up to 9 cups total, until dough is slightly sticky but not excessively wet.

Turn dough out onto a floured surface and knead for about 5 minutes to develop gluten. Form into a compact round shape, place in an oiled bowl, and turn to coat. Cover with a cloth and let rise in a warm area until doubled in size, about 1 hour.

Punch down the dough and knead again until smooth and elastic, about 5 minutes.

Prepare the glaze by whisking 2 teaspoons sugar, 1 egg, 1 teaspoon oil, and 1 teaspoon water. Refrigerate until ready to use.

Cut dough into 4 pieces, then divide each into 3 smaller pieces. Roll into ropes about the thickness of your thumb and 12 inches long. Braid each loaf and place on a prepared baking sheet. Let rise until doubled in size, about 30 to 45 minutes.

Brush egg glaze onto the tops of the loaves and reserve remaining glaze.

Preheat the oven to 350°F (175°C). Bake for 20 minutes, then remove loaves from the oven and brush with remaining glaze. Continue baking until shiny and golden brown, 5 to 10 minutes more.