Combine 2 cups milk and 2 cups water in a medium saucepan. Bring to boil over medium to medium-high heat, but do not scorch. Add grits and cook for 20 minutes on low, stirring often.
Remove from heat and whisk in salt, pepper, butter, and cheese. Fold in diced ham and green onions.
Transfer grits mixture to a casserole dish and refrigerate for at least 3 hours (and up to overnight).
When ready to fry the fritters, heat 3 inches of canola oil to 350˚. Mix teaspoon of water with eggs and whisk well. Pour breadcrumbs into a separate bowl.
Using your hands, roll spoonfuls of the cooled grits into balls about 2 inches across. Dip fritters one at a time first into egg mixture and then into breadcrumbs before frying.
Fry until golden brown, about 3-4 minutes per small batch. Set aside to drain on paper towels before serving.
