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1
Lightly coat a large bowl with vegetable oil and set it aside.
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2
Place the flours, yeast, and salt in the bowl of a stand mixer and whisk by hand to combine; set aside.
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3
Melt the butter in a medium saucepan over low heat.
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4
Add the milk and honey and heat, stirring, until the honey has dissolved and the mixture is warm to the touch but not hot (between 105 degrees F and 115 degrees F on an instant-read thermometer), about 2 to 5 minutes.
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5
Pour the milk mixture over the flour mixture and add the eggs.
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6
Fit the bowl onto the stand mixer and mix with the hook attachment on medium-low speed until just combined, about 2 minutes.
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7
Increase the speed to medium high and knead until the dough is smooth and elastic, about 10 minutes.
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8
(The dough will be sticky.)
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9
Scrape the dough into the prepared bowl and cover tightly with plastic wrap.
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10
Let rise in a warm place until doubled in size, about 1 hour.
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11
(If youre not baking the dough until the next day, place it in the refrigerator to rise overnight.)
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12
Coat the bottom and sides of a 13-by-9-inch glass baking dish with the butter, using all of it; set the dish aside.
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13
(If the dough rose overnight in the refrigerator, let it sit in the bowl at room temperature for 45 minutes before proceeding.)
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14
Transfer the dough to an unfloured work surface and divide it into 20 equal pieces (about 2 1/4 ounces each).
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15
Working with 1 piece at a time, cup your palm over the dough and roll the dough on the work surface into a round, tight ball.
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16
Arrange the balls so that they are just touching in the prepared baking dish, 4 across and 5 lengthwise (they wont touch the sides of the dish).
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17
Cover the baking dish tightly with plastic wrap and let the dough balls rise in a warm place until theyre doubled in size, about 1 hour.
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18
Meanwhile, heat the oven to 350 degrees F and arrange a rack in the middle.
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19
Place the water and egg or honey in a small bowl and whisk to combine.
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20
Uncover the dough balls and brush them with the mixture.
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21
Sprinkle the oats or wheat germ evenly over the tops.
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22
Bake until the bottoms and tops of the rolls are golden brown, rotating the dish halfway through the baking time, about 22 to 25 minutes total.
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23
Transfer the dish to a wire rack and let the rolls cool for at least 10 minutes before serving.
