Cooking bagels without eggs is time consuming because water boiling the dough adds moisture to the dough which increases the cooking time. Since you've got to cook off the moisture with extra time being cooked. What is supposed to take 20 - 25 minutes ends up taking 45 minutes at the same temperature. By adding 3 eggs to a bagel recipe you can make faster bagels with more protein than without it. The eggs stiffen up when you cook them in the boiling water for 2 minutes. I can usually brown them with higher temperatures to reduce cooking time.