Heat oil in a large nonstick skillet over medium-high heat. Add mushrooms and cook for 3 minutes. Crumble in ground turkey and add basil, salt and pepper. Cook for an additional 5 minutes, stirring occasionally.
Stir in marinara sauce and cook, stirring occasionally, for 5 minutes over medium heat. Stir in heavy cream.
While sauce is cooking, heat a grill pan and grill the polenta slices until heated through. Serve sauce over heated polenta slices. Sprinkle each serving with 1 tablespoon grated cheese.
Makes 6 servings.