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Step 1
Stir together warm water, yeast, and 1/2 teaspoon of the sugar. Let stand until foamy, about 5 minutes.
Step 2
Beat milk, egg, salt, yeast mixture, 1/3 cup of the sugar, and 4 tablespoons of the melted butter in a stand mixer fitted with a dough hook attachment on medium-low speed until well combined, about 10 seconds. Gradually add flour, beating until all flour is incorporated. Increase speed to medium; continue beating until dough is smooth and elastic, about 4 minutes. (It will be tacky.) Transfer to a medium bowl lightly coated with cooking spray. Cover with plastic wrap; let stand in a warm place until doubled in volume, 1 to 1 1/2 hours.
Step 3
Stir together cinnamon and remaining 1 cup sugar. Turn dough out onto a lightly floured work surface, and roll into a 20- x 12-inch rectangle. Brush with remaining 3 tablespoons melted butter; sprinkle with cinnamon sugar (reserve 1 tablespoon cinnamon sugar). Cut dough into 5 (12- x 4-inch) strips. Cut each strip into 5 (4- x 2 1/2-inch) rectangles.
Step 4
Lightly coat an 8- x 4 1/2-inch cast-iron loaf pan with cooking spray. Stack dough rectangles on top of each other. Carefully transfer stack to prepared pan with rectangles standing upright (like dominoes). Cover loosely with plastic wrap. Let stand in a warm place until doubled in volume, 45 minutes to 1 hour.
Step 5
Preheat oven to 350°F. Remove and discard plastic wrap. Sprinkle loaf with reserved 1 tablespoon cinnamon sugar. Place pan on a sheet of aluminum foil in oven. Bake until golden brown and a thermometer inserted in center of loaf registers 195°F, 38 to 42 minutes, tenting with aluminum foil after 25 minutes to prevent excessive browning, if needed.
Step 6
Cool in pan on a wire rack 5 minutes. Run an offset spatula around edges of pan to loosen loaf; remove from pan. Serve warm, or cool completely on a wire rack, 1 hour.