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In the bowl of an electric mixer fitted with the dough hook attachment, stir the yeast, water, milk, honey, 2 tablespoons of the butter, egg, and salt until well combined. Gradually add the flour and knead on medium-low speed until the dough pulls away from the sides of the bowl. Turn off the mixer and let the dough rest for 3 to 5 minutes. Continue to knead the dough on medium-low speed for another 5 minutes, or until the dough is soft and smooth. If it seems too sticky, add more flour, 1 tablespoon at a time.
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Transfer the dough to a large greased bowl. Cover and let rise until doubled in size, about 45 minutes.
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Punch the dough down and turn it out onto a lightly floured work surface. Roll the dough into a 1-inch thick rectangle. Cut the dough into 2-inch squares. Transfer the squares to a baking sheet and cover. Let rise until doubled in size, about 45 minutes.
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Preheat the oven to 350F. Bake the rolls for about 15 minutes, or until golden brown.
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To make the honey butter, whisk together the melted butter and honey. Brush on rolls as soon as they come out of the oven.