Step 1

In a 1-quart liquid measuring cup or medium microwave-safe bowl, combine ¾ cup water, the milk, sugar, 57 grams (4 tablespoons) butter and the shortening. Microwave on high for 2 minutes, stirring once or twice; the butter and shortening should be almost fully melted. Remove from the microwave and stir until the fats are fully melted and the mixture is no hotter than 110°F; set aside.

Step 2

In a stand mixer with the dough hook, mix the flour, yeast and salt on low until combined, about 1 minute. With the mixer running on low, slowly pour in the milk mixture. Knead on low until the dough is smooth and elastic and clears the sides of the bowl, 7 to 10 minutes; if the dough sticks to the bowl, add more flour, 1 tablespoon at a time, until it clears the sides.

Step 3

Grease a large bowl with 1 tablespoon of the remaining butter. Shape the dough into a ball and place it in the prepared bowl, turning to coat with the butter. Cover with plastic wrap and let rise in a warm spot until doubled in bulk, about 2 hours.

Step 4

Grease the cups of a 12-cup nonstick standard muffin pan with shortening. Cut each of the remaining 6 pieces of butter in half and place a pat in each prepared muffin cup.

Step 5

When the dough is doubled in bulk, lightly flour the counter. Gently punch down the dough, then turn it out onto the prepared counter. Using a chef’s knife or bench scraper, divide the dough into 12 portions. Using your hands, flatten and shape one dough portion into a rough 2-by-3-inch rectangle, then fold in half crosswise. Place the dough in a prepared muffin cup, the seams facing the sides of the cup; gently tuck in the edges as needed. Shape the remaining dough in the same way. Cover the muffin pan with a kitchen towel and let rise in a warm spot until the rolls have risen above the top of the pan, 30 to 45 minutes. Meanwhile, heat the oven to 400°F with a rack in the lower-middle position.

Step 6

Bake until the rolls are deep golden brown, about 20 minutes. Let cool in the pan on a wire rack for about 5 minutes, then carefully transfer the rolls directly to the rack. Serve warm.