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To make the dough: Weigh your flour; or measure it by gently spooning it into a cup, then sweeping off any excess. In the bowl of a stand mixer fitted with a paddle, combine all of the dough ingredients, mixing just until the dough starts to leave the sides of the bowl. Cover the bowl and let the mixture rest for 15 minutes, for the flour to absorb the liquid; this will make the dough easier to knead.
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After the rest, switch to the dough hook and knead until the dough is smooth and slightly sticky, about 7 minutes.
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Place the dough in a lightly greased bowl or 8-cup measure, cover the container, and let the dough rise for 1 hour, or until it's increased in volume by at least a third.
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To make the filling: Fry (or bake in a 350°F oven for 35 minutes) the bacon until crisp. Drain the bacon and reserve 2 tablespoons of the fat. Place the reserved fat in a large skillet over medium heat. Add the onions and cook for 15 to 20 minutes, stirring occasionally, until golden brown. Remove from the heat and let cool to room temperature. Crumble the cooled bacon and add it to the onions. Stir in the flour and reserved egg white.
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Grease a 9" x 13" pan or two 9" round pans.
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To assemble: Deflate the risen dough and roll it into a 12" x 18" rectangle. Spread the filling over the dough, leaving 1" of one long edge uncovered. Roll up the dough toward the uncovered edge and pinch it closed to seal it.
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Cut the dough into 1" slices; lay them cut side up in the prepared pan(s). Cover and let the rolls rise for about 1 hour, until puffy. Toward the end of the rising time, preheat the oven to 375°F.
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Uncover the rolls and bake for about 25 minutes, until golden brown. Remove from the oven and brush with butter, if desired. Serve warm.
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Store leftovers in the refrigerator; to reheat, tent with aluminum foil and bake in a preheated 350°F oven for about 10 minutes.