- Bring 3 cups of water to a boil in a medium saucepan over medium-high heat.
- Meanwhile, heat olive oil in a large skillet over medium-high heat. Add garlic and onion and cook, stirring, until soft but still crisp—about 5 minutes.
- Add beans and turnip greens, stirring until beans are warm and greens are just wilted but still bright green. Season with salt and pepper. Set aside and keep warm.
- Slowly add grits and ½ teaspoon salt to the boiling water and stir together with a wooden spoon. Decrease heat to medium and cook, stirring until grits are cooked through, about 2 minutes. Stir in milk, cheese, and butter.
- Divide grits among four bowls and spoon butter bean mixture and tomato on top. Serve warm.