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Step 1
Prep the oven and baking dish: Arrange a rack in the middle of the oven and heat to 400°F. Coat a 9x13-inch baking dish with cooking spray or melted butter; set aside.
Step 2
Proof the yeast: Combine the water or milk, sugar, oil, and yeast in the bowl of a stand mixer. Set the mixture aside for 5 minutes to give the yeast a bubbly jumpstart.
Step 3
Mix the dough: Attach the dough hook to the stand mixer. Add 15 ounces (3 cups) of the flour, egg, and salt to the yeast mixture and mix on medium speed for 5 minutes. Add the remaining 5 ounces (1 cup) of flour and mix on medium speed for 10 to 15 minutes to create a sticky dough. At the 6-minute mark during the second mix, the dough should pull away from the sides and slap the sides of the bowl.
Step 4
Divide the dough: Generously flour a work surface. Transfer the dough onto the work surface and divide into 12 equal portions (about 3 ounces each). Loosely roll and fold each portion into a ball, then place them side by side in the prepared baking dish, 4 across and 3 down.
Step 5
Rise the rolls: Cover the dish with a kitchen towel and let the dough rise until doubled in size, about 10 minutes.
Step 6
Bake: Bake until golden brown, 12 to 15 minutes.
Step 7
Finish and cool: While the rolls are still warm, brush the tops with melted butter and sprinkle with additional salt. Remove from the pan immediately to cool slightly before serving.