Add the warm milk, yeast, honey, egg, and melted butter to the bowl of a stand mixer (See the FAQs below for instructions on making the dough without a stand mixer). Whisk until combined
Attach the dough hook and add the flour and salt. Mix on low speed for about 1 minute, until the flour is mostly incorporated. Increase to speed 2 and knead for 7 to 8 minutes, until the dough is smooth, stretchy, and slightly tacky. The dough will still be a bit sticky and will stick slightly to the bottom of the bowl, but it should pull together into a soft dough.
Scrape down the sides, remove the dough from the bowl, and lightly grease the bowl. Return the dough to the greased bowl, cover, and let it rise in a warm place for about 1 hour or until roughly doubled in size
Lightly grease a work surface and your hands. Gently turn the risen dough out onto the greased surface without kneading it again. Divide the dough into 24 equal pieces. (For evenly sized rolls, weigh the entire dough and divide the total weight by 24. Each piece should be around 25 to 27 grams)
Shape each piece into a smooth ball by gently pulling the outer edges underneath and pinching the seam together on the bottom.
Grease a 9×13-inch baking dish and arrange the dough balls seam-side down in 6 rows of 4. Cover loosely and let the rolls rise for about 30 to 40 minutes. Toward the end of the rise time, preheat the oven to 350°F.
Bake the rolls on the center rack for about 13 to 15 minutes, or until the tops are lightly golden brown.
While the rolls bake, make the honey butter by whisking together the melted butter and honey until smooth and combined. As soon as the rolls come out of the oven, brush the tops generously with some of the honey butter. Let the rolls rest together in the pan for about 10 minutes.
While the rolls are resting, cook the chicken nuggets. I prefer to air fry them for the crispiest texture. For Just Bare chicken nuggets, air fry at 400°F for 10 to 12 minutes, or until heated through and crispy.
Gently separate the rolls and slice each one horizontally almost all the way through. Lightly brush the inside of each roll with the remaining honey butter, add one warm chicken nugget, and serve