Heat a large nonstick skillet over medium-high heat. Add oil to pan; swirl to coat. Add turnip, thyme, shallots, and 1/8 teaspoon salt; sauté 2 minutes. Reduce heat to medium-low; cover and cook 6 minutes or until turnips are slightly tender, stirring occasionally. Increase heat to medium-high. Add beans; cook 2 minutes, stirring occasionally. Add remaining 1/4 teaspoon salt, cabbage, 1/4 cup water, vinegar, and pepper; cook 1 minute or until cabbage is slightly wilted, stirring occasionally. Top evenly with cheese.