1. Melt butter in a small saucepan over medium-high heat. Add sausage; sauté 3 minutes, stirring occasionally. Stir in 3 cups milk and 1/4 teaspoon salt; bring to a boil. Add grits; reduce heat, and simmer for 20 minutes or until tender, stirring frequently. Remove from heat; stir in 1/4 teaspoon pepper and cheese.
2. Bring 8 cups water and vinegar to a simmer in a large saucepan. Crack each egg into a small bowl. Gently slide eggs into water; cook 3 minutes or until whites are just set. Remove eggs from water with a slotted spoon.
3. Divide grits evenly among 4 bowls. Top each serving with 1 poached egg; sprinkle eggs evenly with remaining 1/4 teaspoon salt, 1/4 teaspoon pepper, and parsley.