Whisk the warm milk, yeast, and 1 teaspoon of honey in your mixer bowl. Cover it loosely and wait 5 to 10 minutes. The top should look foamy, which tells you the yeast is alive and ready.
Turn the mixer to low and add the remaining honey, egg, yolk, melted butter, 3 cups of flour, and the salt. Mix for one minute, then add the last ½ cup of flour and mix for one more minute. The dough should feel thick, soft, and slightly sticky.
Knead for 8 to 10 full minutes, either in the mixer or by hand on a lightly floured counter. If it sticks too much, add flour one teaspoon at a time. Do the poke test: if the dough slowly bounces back, it is ready.
Place the dough in a lightly greased bowl and turn it once to coat. Cover it and set it in a warm spot for 1 to 2 hours. It is ready when it has doubled in size.
Grease your 9×13-inch pan. Punch down the dough gently to release the air, then divide it into 15 pieces of about 2 ounces (60 g) each. Roll each piece into a smooth ball and set it in the pan.
Cover the pan loosely with plastic wrap. Let the rolls rise for about 1 hour. They should look puffy, touch each other, and have doubled in size.
Preheat your oven to 350°F (177°C). Bake for 20 to 25 minutes, rotating the pan halfway through. If the tops brown too fast, loosely tent them with foil.
While the rolls bake, stir the very soft butter and honey until creamy. Pull the pan out of the oven and spread the topping generously over the warm rolls. Keep a little extra on the side for serving.