Instructions

Adjust oven rack to lower-middle position and heat oven to 200 degrees. When oven reaches 200 degrees, turn it off. Grease large bowl and 13 by 9-inch baking dish. Combine 1¾ cups milk, 6 tablespoons honey, 4 tablespoons butter, and egg in 4-cup liquid measuring cup.
Using stand mixer fitted with dough hook, mix whole wheat flour, all-purpose flour, yeast, and salt on low speed until combined. Slowly add milk mixture and mix until dough comes together, about 1 minute. Increase speed to medium and mix until dough is smooth and almost clears sides of bowl yet still sticks to bottom, 6 to 8 minutes.
Transfer dough, scraping sides of bowl, to greased bowl. Cover with plastic wrap and place in turned-off oven until dough has doubled in size, about 45 minutes.
Punch down dough on lightly floured counter. Divide dough into quarters and cut each quarter into 4 equal pieces. Form each piece into rough ball by pinching and pulling dough edges under so that top is smooth. On clean counter, cup each ball with your palm and roll into smooth, tight ball. Arrange in prepared baking dish and cover loosely with plastic. Let rolls rest in turned-off oven until doubled in size, about 20 minutes.
Remove rolls from oven and discard plastic. Heat oven to 400 degrees. Combine remaining 1 tablespoon butter and remaining 1 teaspoon honey in bowl. Brush rolls with remaining 1 tablespoon milk. Bake rolls until golden brown and register 200 degrees, about 20 minutes, rotating dish halfway through baking. Brush with honey butter and let cool in dish on wire rack for 10 minutes. Remove rolls from dish. Serve.
Make ahead: Instead of 20-minute rise in step 4, baking dish with formed rolls can be refrigerated, covered, for 24 hours. Let dough sit at room temperature for 30 minutes before brushing with milk and baking.