In a small bowl, combine the yeast and water. Let sit for 5-10 minutes until foamy.
In a large mixing bowl, combine the flour, sugar, and salt.
Add the egg and egg yolk, yeast mixture, and half and half. Stir until combined. Dough will be wet; that’s okay.
Let rise for about 2 hours. Dough should be roughly double in size,
When done rising, transfer the dough to a clean well-floured surface.
Roll into a tight ball and then roll into a rectangle about 15x18.
To make the filling, put the brown sugar, cinnamon, and vanilla in a bowl. Add the melted butter and a pinch of salt and stir to combine.
Spread the cinnamon mixture evenly over the dough rectangle. You can use a spatula, but I found it easier to just use my hands.
Carefully roll the dough into an even log.
Using a sharp knife, cut the log into 9 equal sized pieces.
Brush the inside of a square baking pan with butter and transfer the cinnamon rolls to the pan. If you have any filling left, spread it on top of the rolls.
Cover with plastic wrap and put the pan in the fridge.
Refrigerate for 8-16 hours.
When ready to bake, preheat oven to 350 degrees F.
Let the rolls sit at room temperature while the oven is preheating.
Bake for 20-25 minutes, until top is browned.
To make the icing, put all of the ingredients in a bowl and mix using either a stand or hand held mixer until fluffy.
Top the warm rolls with the icing; you may have leftovers.
Notes
Storing leftovers: Leftovers can be stored at room temperature for up to 3 days.