In a small saucepan, heat the milk and butter on medium-low until the butter is melted. Let cool until warm (about 120°F).
In the bowl of an electric mixer, whisk the milk mixture with the yeast, sugar, salt, eggs, and vanilla until well combined. Add in half of the flour and stir roughly with the dough hook to combine.
Attach the dough hook and turn to medium speed. Gradually add the remaining flour until a dough begins to form. Knead until the dough is very soft, smooth, elastic, and doesn’t stick to the sides of the bowl, about 8 to 10 minutes. If the dough is unbearably sticky, add more flour 1 tablespoon at a time. Err on the side of sticky to avoid adding too much extra flour.
Lightly grease a large bowl. Shape the dough into a ball and place in the greased bowl. Cover with plastic wrap and let rise in a warm place until doubled in size, 1 1/2 to 2 hours.
Prepare for dipping:
In a glass measuring cup, microwave the butter in 20-second bursts until melted. In a pie pan or other similarly shaped, wide but shallow dish, use a fork to mix the sugar, cinnamon, and salt, breaking up any clumps.
Assemble the bites:
Lightly grease a 9 by 13-inch baking pan.
Punch down the dough and roll into 1-inch balls. Prioritize speed, don’t worry about being perfect. You should have about 85-90 balls.
Working with 5-6 balls at a time, dunk them in the melted butter, then remove, letting the excess butter drip back in, then roll in the cinnamon sugar. Place in the prepared pan.***
Cover with plastic and let rise until puffy and almost doubled, about 30 minutes.
Meanwhile, preheat the oven to 350°F.
Bake the rolls until lightly golden on top, about 30 minutes.
Make the icing:
While the bites are baking, whisk together all icing ingredients in a medium mixing bowl until very well combined.
Allow the bites to cool for about 10 minutes before drizzling with the icing. Serve warm. Store leftovers in an airtight container for up to 2 days, and gently rewarm before serving.
Notes
*If using active dry yeast instead of instant yeast, you can add it directly to the dough just like instant yeast, but expect the rise time to be about 20% longer.**For best results, use bread flour. You can use all-purpose flour, but note they’ll take longer to proof and won’t be as soft and fluffy.***To make ahead, refrigerate after shaping and coating. Cover tightly and refrigerate. Let sit at room temperature 45-60 minutes before baking.
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