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Pour warm milk into the bowl of a stand mixer fitted with a dough hook attachment. Or, if you do not own a stand mixer, a regular large mixing bowl. Sprinkle yeast and 1/2 teaspoon sugar on top of the milk. Give it a light stir with a spoon and allow to sit for 5 minutes. The mixture should be frothy after 5 minutes. If not, start over with new yeast.
With the stand mixer running on low speed, add the honey, egg, egg yolk, melted butter, salt, and 3 cups of flour. Beat on low speed for 1 minute, then add remaining 1/2 cup of flour. Beat on low speed for 1 minute as it all combines. The dough should be thick, yet soft. And only slightly sticky. It should pull away from the sides of the bowl as it mixes. When it does, it is ready to knead. If, however, the dough is too sticky to handle– add more flour, 1 Tablespoon at a time. Make sure you do not add too much extra flour; you want a soft, slightly sticky dough.
Form dough into a ball and turn it out onto a lightly floured surface. Knead for 2 minutes, then place into a greased bowl– I usually just use olive oil or nonstick spray. Turn the dough over to coat all sides. Cover the bowl with plastic wrap and place it in a warm environment to rise until doubled, about 2 hours. For this warm environment, I preheat the oven to 200°F (93°C) then turn the oven off and place the bowl inside the warm-ish oven.
Once doubled in size, punch down the dough to release any air bubbles. Remove dough from the bowl and turn it out onto a lightly floured surface. Punch down again to release any more air bubbles if needed. Using a sharp knife, cut the dough in half. Cut each half into 8 equal pieces for a total of 16 pieces that are about 1/4 cup each– golfball size, give or take. They don’t need to be perfect! Shape into balls as best you can and arrange in a greased 9×13 baking pan. Loosely cover with plastic wrap and allow to rise until doubled in size and puffy, about 1 hour.
Preheat oven to 350°F (177°C). Bake the rolls for 18-21 minutes until the tops are golden brown and the edges of each roll look cooked. While the rolls bake, mix the topping ingredients together to make a creamy honey butter. Remove the rolls from the oven when they are done and brush or spread a generous amount of honey butter onto each warm roll. Serve with any remaining honey butter.
Cover leftovers and keep in the refrigerator for up to 1 week or freeze for up to 3 months, then thaw overnight in the refrigerator. Warm up in a 300°F (149°C) oven for 10 minutes.