*my personal preference is 1/2 cup finely ground and 1/2 cup medium ground corn meal
Bring the milk, 2 cups of the water, and a very large pinch of salt to a boil in a medium saucepan. Reduce heat to a low simmer and add cornmeal in a slow and steady stream, constantly whisking to prevent lumps.
Polenta should be at a bare simmer, and cook for 15 minutes, stirring occasionally. If the mixture gets too thick (mine did), add water, 1/2 cup at a time. I ended up doing this twice.
Remove from heat, stir in butter and olive oil, and then stir in cheddar cheese. Season with Kosher salt and freshly ground black pepper.