Combine milk, water, and salt in a medium saucepan; bring to a boil over medium heat. Add grits, stirring well. Reduce heat; cover and cook 10 minutes, stirring occasionally. Add butter and Cheddar cheese; stir until melted. Cool 10 minutes
Scoop grits into a serving bowl using an ice cream scoop. Combine Parmesan cheese and paprika; mix well. Sprinkle cheese mixture over tops of scoops just before serving.