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Place 4 cups of the flour, sugar, yeast, and salt in the bowl of a stand mixer fitted with the hook attachment and whisk to combine. (Alternatively, place in a large bowl if kneading by hand.)
Place the water, oil, eggs, and egg yolk in a medium bowl and whisk to combine. Turn the mixer speed onto low, and slowly pour in the egg mixture. Increase the speed to medium-low and beat until the dough is smooth, soft, and holds a ball shape, 8 to 10 minutes. If after 4 minutes the dough doesn't clear the side of the bowl, add more flour a tablespoon at a time until it clears but still sticks to the bottom of the bowl. (If kneading by hand, stir until the dough comes together, then knead on a floured work surface.)
Coat a large bowl with cooking spray. Transfer the dough to the bowl and cover tightly with plastic wrap. Let rise in a warm place until nearly doubled in size, about 1 1/2 hours.
Coat a 9x13-inch baking dish with cooking spray; set aside. Divide the dough into 15 pieces (about 2 1/2 ounces each).
Using your hands, roll 1 piece into a 10-inch-long rope (if the dough is sticky, lightly flour your hands and not the work surface, as that will make it harder to roll). If the rope shrinks a lot as you try to roll it, let it rest for 5 minutes to relax the gluten and then try again.
Tie the rope into a knot. Take the end of the rope that went through the center of the knot, pull it over the side of the knot, and tuck it underneath.
Take the other end of the rope and pull it up and over the side of the knot, then press the end firmly into the center of the knot. Place in the baking dish.
Repeat with the remaining pieces and arrange the rolls in the baking dish, 5 across and 3 down.
Cover with oiled plastic wrap and set aside to rise in a warm place until puffed and about doubled in size, about 1 hour. About 30 minutes before the rolls are ready, arrange a rack in the lower third of the oven and heat to 350°F. Beat the egg white with the water for the egg wash and set aside.
Uncover the rolls and brush with a thin layer of the egg wash. Bake the rolls 15 minutes. Rotate the baking dish from front to back and bake until the bottoms and tops of the rolls are golden-brown, about 15 minutes more (metal baking pans will bake faster than glass or ceramic, so check on them earlier). Place the pan on a wire rack and let cool at least 15 minutes before serving.