Combine the milk and water in a saucepan and bring to a boil. Stir in the grits, and reduce heat to low. Cover, and cook for 20 to 30 minutes until thickened and creamy. Stir the grits occasionally while cooking. When the grits are finished, stir in the cheddar cheese until melted.
In the meantime, prepare the blackened seasoning by combining the smoked paprika, garlic powder, onion powder, oregano, thyme, cayenne, pepper, and salt. Add the olive oil to a mixing bowl and whisk in the blackened seasoning. Put the green beans in the bowl and toss until well-coated.
Heat a large cast iron or other skillet over medium-high heat. Add the green beans, and cook for 10 to 15 minutes, stirring occasionally, until blackened and tender.
Serve the green beans on a pile of cheesy grits, and dig in!