In a Dutch oven, bring the chicken broth, oil, garlic and 1 1/2 cups water to a boil over medium-high heat. Reduce the heat to medium low and whisk in the polenta. Season with 1/2 teaspoon salt and cook, stirring occasionally with a wooden spoon, about 10 minutes. Stir in the Parmesan, mascarpone, pecorino and butter. Cook, stirring often, about 5 minutes. Fold in the spinach and cook until wilted, about 5 minutes longer. Add 1/4 cup water if the mixture gets too thick.
Pour the polenta into a large bowl and serve with grated Parmesan over the top.