8 Tbsp (1 stick)unsalted butter, melted and divided
2large eggs, at room temperature
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Instructions
Preparing the Ingredients
In a small saucepan, add in ¼ cup of flour. Slowly pour in milk, whisking constantly, until smooth.
1 ¼ cup whole milk
Set saucepan over medium heat. Heat mixture, whisking constantly, until it forms a thick paste (about 5 to 8 minutes).
Transfer flour paste into the bowl of a stand mixer fitted with the dough hook attachment. Set aside to cool for at least 10 minutes.
Meanwhile, in a small bowl, dissolve yeast and ½ Tbsp sugar into warm water. Set aside until the top begins to foam.
2 ¼ tsp active dry yeast
¼ cup warm water
In a large bowl, whisk together the remaining 3 ¼ cup flour, 2 Tbsp of sugar, and salt. Set aside.
1 tsp kosher salt
Forming the Dough
Into the bowl of the stand mixer with the cooled flour paste, add in 1 egg, 6 Tbsp of melted butter, yeast mixture, and flour mixture.
Using the dough hook attachment, mix on medium speed until the dough forms a smooth mass and pulls away from the sides of the bowl, adding in 1 to 2 Tbsp of additional flour, as necessary. (The dough will be tacky, but not overly sticky.)
Pour the dough onto a lightly floured surface and knead it into a smooth ball. Place the ball of dough into a large bowl greased with melted butter. Cover with a damp kitchen towel or plastic wrap and set in a warm place. Allow the dough to rise until doubled in volume (about 90 to 120 minutes).
Forming the Rolls
Grease a 9" by 13" baking pan with some of the remaining melted butter. Set aside.
Pour the dough, once again, onto a lightly floured surface and divide into 12 roughly equal parts. Form each into a smooth ball, pinching any seams closed with your fingers.
Arrange each dough part, seam side down, into the greased baking pan, as desired. Cover with a damp kitchen towel or plastic wrap and set, once again, in a warm place. Allow the dough to rise for a second time until they become puffy (about 60 minutes).
Baking the Rolls
Preheat oven to 350℉.
In a small bowl, beat the remaining egg with 1 Tbsp of water. With a pastry brush, brush each roll with the egg wash.
Bake the rolls, in the center of the oven, until the tops are golden brown (about 20 to 25 minutes).
Remove the rolls from the oven and brush them with the remaining melted butter.
Serve warm, or allow to cool completely and store in an airtight container at room temperature.
Notes
Make them ahead: You can form the dough and set it, covered, in the refrigerator overnight for its first rising. When ready to use, remove the dough from the refrigerator and begin forming the rolls. Note that the second rising will likely take a bit longer, since the dough will need to come back up to room temperature. (It is especially important to keep the rolls covered during this second rising so they don't dry out!)