Add all of the ingredients except the 2 large eggs into a stand mixer fitted with a dough hook. Mix on low until everything combines, then slowly bring up the speed to medium-high until the dough becomes smooth and elastic. (If you don't see everything becoming fully incorporated after a few minutes, add water, one tablespoon at a time until it comes together.)
Lightly coat a bowl with oil and place the dough inside. Cover with plastic wrap, then place the bowl in a plastic bag. Place in a warm, dry area for 1½ hours.
Deflate the dough and transfer to a very lightly floured surface. Divide into four equal pieces. Roll each piece to about 18 inches in length.
Form a two-strand braid. You can do this by making an "X" with two of the ropes. Take two opposite ends of the "X" and fold over so the end that was on the bottom is now on the top and vice versa for the top end. Repeat with the other two ends. Keep repeating this until you can't any longer. Turn this bundle onto it's side and gently stretch to show the braid. Take the small end, which should be the end with the ends of the ropes and press together and tuck under the braid. Repeat with the other two ropes.
Brush the loaves with the beaten eggs. Cover and rise for an hour. While the loaves are rising, preheat the oven to 350 degrees F. Brush again with the eggs and bake for 45 minutes to an hour. The bread should be a dark brown and sounds hollow when you tap on it. Transfer to a wire rack to cool completely.