In the bowl of a stand mixer, whisk together the warm water, 2 tablespoons diced butter, granulated sugar, the egg, kosher salt, and yeast.
Attach the dough hook and add the flour. Knead on low speed until all of the ingredients come together, about 2 minutes. Increase the speed to medium and continue to knead until the dough starts to pull away from the side of the bowl, about 8 minutes.
Lightly oil a large bowl and transfer the dough to it. The dough will be very sticky. Cover the bowl with plastic wrap or a clean dish towel and let rise until the dough doubles in size, about 1 to 2 hours.
Melt the remaining 3 tablespoons butter and set aside. Scoop the dough onto a well-floured counter, and use floured hands to pat the dough into a 12×9-inch rectangle. Cut the dough into desired number of rolls.
Shape each square into a round and dip both sides lightly in melted butter. Transfer the rounds to a 9×13-inch baking sheet, lining the rolls up with room to expand.
Let the dough rise again until the rolls are puffed up and springy, about 50 minutes to 1 hour. Heat oven to 400°F.
Bake the rolls until the tops are golden brown, 10 to 14 minutes. Remove from the oven and brush immediately with remaining melted butter. If you used unsalted butter, sprinkle the tops with a few pinches of flaky salt (optional).
Eat right away or rewarm before serving. These rolls keep best in the freezer if you’re saving them for future.