In the bowl of an electric mixer, whisk together the milk, sugar, egg, egg yolk, and melted butter. Stir in the flour, instant yeast, and salt with a wooden spoon until everything comes together into a ball of dough.
Knead with the dough hook on medium for 8 minutes. Alternately, knead by hand for 8-10 minutes on a floured surface. Lightly oil and large bowl and place the dough inside.
Cover the dough with plastic wrap and a kitchen towel and let rise for 1 to 1.5 hours or until doubled in size.
Melt the butter and set aside. In a small bowl, mix together the sugar and cinnamon.
Shape the balls. Punch the dough down and divide and roll into small balls, about 1 to 1 1/4 inch in diameter. If you want to be precise about it, each ball should weigh about 15 grams.
Dip the balls into the butter, then roll in the cinnamon sugar mix. Place each coated ball into your pan, repeating until you finish all of the dough. Cover the pan with plastic wrap and let rise for 20 minutes. Meanwhile, preheat the oven to 350°F.
Optional: While the oven is warming up, mix the butter with 2-4 extra tablespoons of melted butter, 1/4 cup brown sugar, and 1/2 tsp vanilla. Just before you put the cinnamon bites into the oven, pour the cinnamon sugar syrup evenly over the balls of dough.
Bake for 35-45 minutes or until golden brown and cooked through. Cover with foil if the top starts browning too quickly. When baked through, pull from the oven and cool in the pan for 5-10 minutes.
Make the icing by whisking all of the icing ingredients together. Drizzle on generously and enjoy the cinnamon bites warm.