Make the dough: Make a mound out of the flour on a clean surface or in a large mixing bowl and make a well in the center of the pile. Lightly beat together the egg, salt, oil, and water in a separate bowl. Drop this mixture into the flour well and work the mixture with a fork or your hands, folding the flour over the egg mixture until a dough comes together and can be rolled into a ball. Knead this mixture by folding the dough over towards the body and press with the heel of the hand and give a slight turn. The mixture will feel a bit dry but as you continue to knead it it will hydrate. Fold, press and turn the dough again and continue this process until the dough is smooth and elastic. Knead the dough for about 15 minutes. Divide the dough into 2 balls and set aside, uncovered, for 30 to 45 minutes. 

Preheat the oven to 350°.

Shape and toast the egg barley: Grate the balls of dough on the coarse side of a box grater onto a parchment lined baking sheet. Grate the dough in a one direct motion from the top of the grater to the bottom. Try to keep the grated dough in an even layer on the sheet. Transfer the baking sheet with the grated dough into the oven and bake it for 20 minutes total, checking every 5 to 10 minutes, stirring the barley and breaking apart any large chunks of egg barley. The barley is finished when most of the pieces are golden brown and very dry. If the barley is not evenly toasted that's completely fine. The uneven toast allows the barley to have different flavors. 

Cook the egg barley: Add the schmaltz to a medium size pot and melt it over medium heat. Add the onion, bay leaf,  ¼ teaspoon salt and the black pepper.  Cook the onions until they are translucent, for about 5-10 minutes. Add the garlic and cook for 1 more minute. Add the toasted barley, stir to coat the barley with the onions and schmaltz that are in the pan.  Add the stock, bring the mixture to a boil then place a lid on the pot and reduce the heat to medium-low or to a gentle simmer.  Allow it to simmer until the liquid has been absorbed and the barley is tender, about 20 minutes.  If more liquid is needed add more stock or water and continue to cook.