Bring 2 cups of water, the milk and a very large pinch of salt to a boil in a medium saucepan. Reduce the heat so the liquid is at a low simmer, and add the cornmeal in a slow and steady stream, constantly whisking to prevent lumps. Cook the polenta at a low simmer, stirring occasionally, for 15 minutes; if the mixture gets too thick, add water 1/2 cup at a time.
Remove from the heat, stir in the butter and olive oil and then stir in the Cheddar. Season with kosher salt and freshly ground black pepper.
Serve immediately in mini cups, topped with chopped herbs