Kale and Mushrooms with Creamy Polenta

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

cup freshly grated Parmesan cheese