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In a large bowl or the bowl of your stand mixer, combine the water, milk, butter, sugar, salt, and yeast. Stir well and let sit for 6 to 8 minutes, or until you see the yeast begin to foam.
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Add 5 cups (600g) of flour and mix by hand or with the flat beater attachment until the dough forms a rough, shaggy mass. The dough will not form a ball at this point — it will be just shy of coming together.
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Add flour, 1/2 cup at a time, and mix with a spatula or the dough hook until a smooth ball begins to form. Knead by hand for about 10 minutes, or by machine for 4 to 5 minutes, until a soft, smooth ball of dough is formed. The dough should feel elastic and slightly tacky to the touch.
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Transfer the dough to a lightly greased bowl, then turn so that the dough is lightly greased. Cover with plastic wrap or a shower cap and let rise for 20 minutes at room temperature, or until the dough is full and puffy.
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On a clean work surface, gently deflate the dough and pat out to a rough rectangle about 8" by 12". Cut the dough into 4 long strips, then cut each strip into 6 portions for a total of 24 dough balls. Working with lightly greased hands, shape each ball into a tight round by using your cupped hands to roll the dough against the work surface. Lightly sprinkle flour, as necessary, to prevent sticking.
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Place the shaped rolls in any of the following pans, well-greased or lined with parchment: one half-sheet pan or 2 quarter-sheet pans; two 9" x 13" pans; four 8" or 9" round baking pans; or a combination of any. (See "tips," below for details on baking your rolls on a bed of grated cheese.)
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After the rolls are in the pans, cover and let rise at room temperature for another 20 to 25 minutes, or until well rounded and full looking. If you are baking now, preheat the oven to 350°F. (See "tips," below for instructions on freezing unbaked buns.)
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Bake for 20 to 25 minutes, or until the quick dinner rolls are golden brown and an internal thermometer reads 190°F. For added flavor and a satiny-soft finish, brush the baked rolls with melted butter. Serve warm. Store leftovers in an airtight container and room temperature for up to 3 days.