In a large mixing bowl of a stand mixer dissolve the yeast in the warm water. Add the warm milk, sugar, and eggs. Add the dough hook attachment, and stir in the flour and salt. Scrape the bottom and sides of the bowl occasionally with a rubber spatula. Cut the butter into small pieces and incorporate into the dough. Scrape the bowl a few times. Beat the dough until it becomes smooth, about 5-7 minutes.
Turn the dough out onto a floured work surface and knead for 5-6 minutes, making a smooth dough. This dough is going to be sticky when you turn it out. After kneading, shape into a round ball and place back into the greased mixing bowl. Cover loosely with plastic wrap and drape with a clean kitchen towel. Place in a warm area and let rise until doubled in size, about 1 hour.
Turn the dough out onto a lightly floured work surface and knead the dough for a few minutes. Turn back into the greased bowl (spray with cooking spray again if needed) and let rise again until doubled, about 1 hour.
Turn the dough out onto a floured work surface and roll out with a rolling pin. Making it into a rectangle shape, about ¼ to ½-inch thick. Spread the melted butter evenly with a pastry brush. Sprinkle the brown sugar and granulated sugar evenly over the melted butter. Sprinkle generously with ground cinnamon.
Roll up, starting at the long end fairly tight. Brush the edge of the dough with melted butter and press to seal. Cut the dough into 2 inch rolls.
Place the cinnamon rolls evenly into greased cast iron pans or a half sheet pan lined with parchment paper. Cover the pan loosely with plastic wrap and a clean kitchen cloth and let rise until doubled, about 30 minutes to 1 hour.
While they are rising, whisk together your icing. Cover with plastic wrap and set aside. You want it to be fairly thick.
Preheat the oven to 350 degrees F. Once the cinnamon rolls have doubled in size, brush gently with an egg wash. Place the cast iron pan in the preheated oven and bake for 25-30 minutes. Let cool on a baking rack for 15 minutes before spooning the icing over top the cinnamon rolls.