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Warm the milk in a microwave for 45 seconds. Pour into a stand mixer bowl with white sugar, yeast and vinegar. Let proof for 5 minutes.
Add the brown sugar, salt, flour and 2 tablespoons butter to the proofed yeast. Using a stand mixer with a dough hook, knead the dough at speed 2 for 30 seconds. Increase speed to 4 and knead for 5 minutes.
NOTE: If you knead the dough by hand, avoid the temptation to add more flour. The dough will be sticky. It will soften the longer you knead it.
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Dump the dough onto the counter and cover with the mixing bowl. Let rise for 1 hour. Punch down, knead a few times and re-cover. Let rise another hour.
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Punch down and cut and shape into 12 equal-sized rolls (about 60 grams each). Place on a silpat-lined baking sheet. Brush with melted butter. Cover loosely with plastic wrap and let rise 30 minutes.
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Bake in a 400-degree oven for 12-15 minutes.