01 -
Add the sliced unsalted butter, granulated sugar, and kosher salt to the bowl of a stand mixer. Warm 1 1/4 cups whole milk in the microwave until between 105-110°F and pour 1 cup into the mixer bowl without stirring; let it sit.
02 -
Stir 2 1/4 teaspoons active dry yeast into the remaining 1/4 cup warm milk and let sit for 5 minutes until foamy. Add to the mixer bowl along with the beaten egg and combine.
03 -
Using the hook attachment, gradually add 3 1/2 cups all-purpose flour, one cup at a time, scraping down the sides as needed. Once a dough forms, knead on medium-high speed for 3 minutes, adding up to 1/2 cup more flour if the dough sticks excessively.
04 -
Transfer the dough to a large bowl coated with 1 teaspoon vegetable oil. Turn dough to coat in oil, cover tightly with plastic wrap, and let rise in a warm place for 1 to 2 hours until doubled in size.
05 -
Melt 1/4 cup unsalted butter and brush a 9" x 13" baking dish lightly with the melted butter; set aside.
06 -
Punch down the risen dough to release air. Divide into 15 equal portions. Shape each into a smooth ball by stretching and tucking the dough, pinching seams closed, and gently rolling between your hands.
07 -
Place the dough balls seam-side down in the prepared baking dish in 5 rows of 3. Cover with plastic wrap and let rise for about 1 hour until doubled in size.
08 -
Preheat oven to 350°F. Remove plastic wrap and bake rolls for 20 to 25 minutes until golden brown and hollow sounding when tapped.
09 -
Brush the hot rolls immediately with the remaining melted butter and serve warm.