Start by combining the warm water in a large mixing bowl with 1 teaspoon of sugar and the yeast. Give it a little stir, then let it sit for 5-10 minutes until the yeast gets foamy. If the yeast doesn't foam up and bubble a bit, it's probably old and you should get some new yeast and start over.
Once the yeast is foamy, go ahead and add the rest of the sugar, warm milk, egg, salt, melted butter, vanilla extract, and about half of the flour. Stir or mix together well to combine. You can make this in a stand mixer using the paddle attachment for this part before switching to the dough hook to knead, but you can also do this by hand.
Dump the rest of the flour into the dough and continue to mix together until it forms a ball. Knead the ball with a dough hook for 3-5 minutes or turn it out onto a floured surface and knead by hand for 5-8 minutes until pretty smooth and not too sticky. You may need to add a little extra flour if kneading by hand to keep it from sticking too much to the surface you are kneading the dough on.
Shape the dough into a ball then place in a lightly greased bowl and cover with plastic wrap. Let it rise for 1 to 1 ½ hours until doubled in size.
In another bowl, combine melted butter, brown sugar, granulated sugar, ground cinnamon and cornstarch. Stir with a fork until evenly distributed and the texture of wet sand.
Turn the dough out onto a lightly floured surface and roll it out into a large rectangle that is roughly 9x12 inches.
Sprinkle the cinnamon sugar filling over the dough. Slice into six even strips, then roll each strip up to make a cinnamon roll. You could also roll the whole thing into a log and then slice into 6 cinnamon rolls using a sharp serrated knife, unflavored dental floss, or a thread, but lately I have been enjoying this strip approach. Both work well.
Transfer to shaped cinnamon rolls to an 8-inch round pan that has been sprayed with baking spray, spacing them evenly around the pan with one in the center. (This is the point to cover the cinnamon rolls with plastic wrap and stick them in the fridge overnight if you want to make them ahead.) Cover loosely with plastic wrap and let rise in a warm spot for 45-60 minutes until puffy. Preheat the oven to 375°F while the rolls are rising.
Remove the plastic wrap and bake the cinnamon rolls for 22 to 26 minutes until golden brown.
Make the frosting by beating the softened butter, cream cheese, powdered sugar, vanilla, and just enough of the milk to make a smooth, spreadable icing.
Let the cinnamon rolls cool in the pan for 5-10 minutes before frosting with the icing. Serve warm.