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Special equipment: two 12-cup muffin tins
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Warm 1/4 cup of the milk in a small saucepan over medium-low heat to anywhere between 100 and 115 degrees F. Pour the milk into the bowl of a stand mixer fitted with a hook attachment.
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Add the sugar and yeast, and let stand until foamy, about 5 minutes.
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Add the softened butter, half the flour, half the remaining milk and fine salt.
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Mix on medium-high speed just to incorporate.
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Add the egg, mix until fully incorporated, then add the remaining flour and milk.
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Knead with the hook on medium-high speed until the dough is smooth and pulls away from the sides, about 5 minutes (the dough will still be sticky).
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Lightly butter a large bowl with some of the melted butter, and turn the dough out into it.
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Cover with plastic wrap, and let stand in a slightly warm place until doubled in size, about 2 hours.
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Lightly butter two 12-cup muffin tins with some of the melted butter.
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Punch the dough down.
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Divide it into 24 even pieces, and roll them into rough balls.
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Roll each ball in the melted butter to coat, letting the excess drip off, and plop it into a muffin cup.
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Cover lightly with plastic wrap, and let rise in the refrigerator at least 8 hours and up to 1 day.
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Position oven racks in the lower and upper thirds of the oven, and preheat to 375 degrees F. Remove the tins from the refrigerator, and let stand at room temperature 1 hour (the dough won't puff up significantly).
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Sprinkle evenly with sea salt, and bake, rotating the tins halfway through, until just lightly golden but still rather pale and almost cooked through, 10 to 15 minutes.
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Let the parbaked rolls cool slightly in the tins, then transfer to cooling racks to cool completely.
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Pack them in resealable plastic bags, label and date, and freeze for up to 2 weeks.
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To serve, preheat the oven to 350 degrees F. Bake the frozen rolls on a parchment-lined baking sheet until warmed through and golden brown on top, about 20 minutes.
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Brush the warm rolls with melted butter.