Start the dough. Add the warm milk, yeast, and 1 Tablespoon of the sugar to the bowl of a stand mixer and whisk together. Cover the bowl and leave the mixture for 5 minutes. If you do not have a stand mixer, use a large mixing bowl and combine the dough by hand with a sturdy wooden spoon or silicone spatula. A hand mixer is less suitable because this sticky dough tends to climb into the beaters.
Mix. Add the remaining sugar, egg, butter, salt, and 1 cup of the flour. Using the dough hook or paddle attachment, mix on low speed for 30 seconds. Scrape down the bowl, add the remaining flour, and continue mixing on medium speed for about 2 minutes, until the dough forms and begins pulling away from the sides. If it is so wet that it cannot reasonably be kneaded, add additional flour 1 Tablespoon at a time. The finished dough at this stage should remain soft and slightly sticky while still being manageable with lightly floured hands.
Knead. Continue kneading with the mixer for 5 full minutes, or transfer the dough to a lightly floured work surface and knead it by hand for 5 full minutes. If excessive sticking develops, add flour only 1 teaspoon at a time, either to the dough or the kneading surface. Avoid adding more than necessary, since the dough should remain soft and slightly tacky rather than becoming dry. To check it, press the dough with a finger; it should gradually spring back. You can also perform a windowpane test by stretching a golfball-size piece very thin. When it can stretch enough for light to pass through without tearing first, kneading is complete.
First rise. Lightly coat a large bowl with oil or nonstick spray. Put the dough into the bowl and turn it so all sides receive a light coating. Cover with aluminum foil, plastic wrap, or a clean kitchen towel. Leave it in a relatively warm place for 1–2 hours, or until doubled in size.
Prepare the pan. Grease a 9×13 inch baking pan or two 9-inch square or round baking pans. A cast iron skillet or lined baking sheet can also be used.
Form the rolls. Punch down the risen dough to remove trapped air. Divide it into 14–16 equal pieces; exact uniformity is not necessary. Shape each portion into a smooth ball and place the balls in the prepared pan.
Second rise. Cover the shaped rolls with aluminum foil, plastic wrap, or a clean kitchen towel. Let them rise for about 1 hour, until noticeably puffy.
Heat the oven. Move an oven rack to a lower position and preheat the oven to 350°F (177°C). Baking toward the bottom of the oven helps prevent the tops from becoming too dark.
Bake. Bake the rolls for 20–25 minutes, rotating the pan halfway through the baking time. They are ready when the tops are golden brown. If they begin browning too quickly, loosely cover the pan with aluminum foil. Remove from the oven and, if using it, brush the warm rolls with the honey-butter topping. Let them cool for a few minutes before serving.
Store. Keep leftover rolls tightly covered at room temperature for 2–3 days, or refrigerate them for up to 1 week.