1 1/4 pounds kale, stemmed, cut into 1-inch pieces
4 cups whole milk
3 1/2 cups water
2 cups polenta
1/2 teaspoon salt
3/4 teaspoon ground black pepper
4 ounces pancetta (Italian bacon) or bacon, coarsely chopped
4 ounces mushrooms (such as crimini, oyster, and stemmed shiitake), sliced
4 tablespoons extra-virgin olive oil, divided
1 garlic clove, minced
1/2 cup low-salt chicken broth
2 tablespoons chopped fresh thyme
1 tablespoon grated lemon peel
4 tablespoons unsalted butter
2/3 cup freshly grated Parmesan cheese