Take 1/4 cup unsalted butter and slice it as thin as you can, add the slices to the bottom of a stand mixer. Add ¼ cup granulated sugar and 1 teaspoon kosher salt to the mixer.
Warm 1 ¼ cups whole milk milk in a microwave safe bowl in the microwave. I like to do this in 15-30 second intervals. The temperature of the milk should be between 105-110°F (do not warm to over 110°F). Pour 1 cup of the warm milk into the bowl with the butter, no need to stir, just let it sit.
Add 2 ¼ teaspoons (1 packet) active dry yeast to the remaining 1/4 cup milk and give it a stir. Let it sit for about 5 minutes, until foamy. Add this mixture to the mixer. Add in 1 large egg, beaten and stir everything to combine.
Using the hook attachment, start stirring in 3 ½ cups all-purpose flour (one cup at a time), scrape down the sides as needed.
Do this until you add 3 and ½ cups of flour. Once the mixture resembles a dough, turn the speed to medium-high and start to knead it.
If the dough doesn’t start to cleanly pull away from the sides of the bowl, add a little flour at a time (up to a half cup) until the sides of the bowl are clean, if the dough is still attached at the very bottom of the bowl that’s okay. Continue to knead for 3 minutes.
In a large bowl, add 1 teaspoon vegetable oil. Take the dough out of the mixer and add it to the bowl with the oil, turn it around in the oil so it is coated. Cover with plastic wrap and let it rise in a warm place for 1-2 hours until doubled in size.
Melt 1/4 cup unsalted butter. Brush a 9"x 13" baking dish with some of the butter. You will only need a small amount. Set aside.
Punch down the dough to release the air bubbles.
Divide the dough into 15 sections. Take each dough ball with your hands and stretch it out, tuck the ends of the dough around itself to form a smooth ball and pinch the seams together, gently roll it between your hands to form a ball.
Place the ball seam side down into the prepared baking dish, 5 rows of 3 rolls. Cover again with plastic wrap and let them double in size, about 1 hour.
Preheat the oven to 350°F. Take the plastic wrap off the baking dish and bake for 20-25 minutes until the tops are golden brown and when tapped the rolls sound hollow.
Immediately brush the rest of the melted butter all over the hot rolls then serve.
Video
Notes
These can be made without a stand mixer, see my tips above.
You can freeze these before or after baking.
Add in some additions to flavor these rolls if desired, I gave some ideas above.