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1. In a medium saucepan combine the milk, butter, sugar, and salt. Heat over low heat until warm (105 degrees F to 115 degrees F). Remove from heat. Stir in yeast until dissolved. In a large mixing bowl lightly beat the egg with a fork. Add the milk mixture and 1 1/2 cups of the flour. Beat with an electric mixer on low speed for 1 minute, scraping sides of bowl constantly.
2. Using a wooden spoon, stir in enough of the remaining flour to make a soft dough that just starts to pull away from the sides of the bowl (dough will be slightly sticky). Transfer dough to a lightly greased large bowl. Cover; let rise in a warm place until nearly double in size (1 to 1 1/2 hours).
3. Punch dough down. Turn dough out onto a lightly floured surface. Divide dough in half. Cover; let rest for 10 minutes. Meanwhile, lightly grease two 8x4x2-inch foil loaf pans. In a small bowl stir together the melted butter, mustard, and hot pepper sauce.
4. On a lightly floured surface, roll one dough half into a 20x12-inch rectangle. Brush with half of the butter mixture. Sprinkle evenly with half of the cheese and onions. Cut the dough crosswise into 6 equal strips. Stack the strips. Cut the stacked strips crosswise into 6 equal pieces. Arrange the stacked pieces next to each other, cut sides up, in a loaf pan.* Repeat with remaining dough, butter mixture, cheese, and onions. Sprinkle any spilled cheese and onions on top and drizzle with any remaining butter mixture. Cover; let rise in a warm place for 30 minutes.
5. Preheat oven to 350 degrees F. Bake for 40 minutes, covering loaves with foil the last 15 minutes of baking to prevent overbrowning. Cool in pans on a wire rack. Wrap loaves in pans. Attach directions for reheating loaves.