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1
Stir together sugar and milk in a small bowl.
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2
Sprinkle yeast over mixture and let stand until foamy, about 10 minutes.
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3
Stir flour into yeast mixture, forming a soft dough, and cut a deep X across top.
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4
Let starter rise, covered with plastic wrap, at room temperature, 1 hour.
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5
Combine salt, sugar, and hot milk in a small bowl and stir until salt and sugar are dissolved.
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6
Fit mixer with whisk attachment, then beat 2 eggs at medium-low speed until fluffy.
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7
Add sugar mixture and beat until combined well.
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8
With motor running, add in order, beating after each addition: 1/2 cup flour, remaining egg, 1/2 cup flour, about one fourth of butter, and remaining 1/2 cup flour.
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9
Beat mixture 1 minute.
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10
Remove bowl from mixer and fit mixer with dough-hook attachment.
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11
Spread starter onto dough with a rubber spatula and return bowl to mixer.
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12
Beat dough at medium-high speed 6 minutes, or until dough is smooth and elastic.
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13
Add remaining butter and beat 1 minute, or until butter is incorporated.
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14
Lightly butter a large bowl and scrape dough into bowl with rubber spatula.
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15
Lightly dust dough with flour to prevent a crust from forming.
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16
Cover bowl with plastic wrap and let dough rise at room temperature until more than doubled in bulk, 2 to 3 hours.
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17
Punch down dough and lightly dust with flour.
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18
Cover bowl with plastic wrap and chill dough, punching down after first hour, at least 12 hours.
