6 ounces Thomasville Tomme cheese or Georgia Gouda, rind removed and cut into 1/4-inch cubes
6 cups canola or peanut oil, for frying
1/3 cup all-purpose flour, for frying
In a medium saucepan over high heat, bring 2 cups water, milk, and 3/4 teaspoon salt to a boil. Reduce heat to medium and slowly add grits in a stream, whisking constantly to avoid lumps.
Reduce heat to low and add heavy cream. Cook over low heat, stirring frequently, until grits are completely soft, about 50 to 60 minutes. Remove from heat, stir ham into grits, and let grits cool completely. (Grits can be cooked up to a day ahead and stored, covered, in refrigerator.)
Using a small ice-cream scoop or a spoon, scoop up about 2 teaspoons grits. Insert a cube of cheese into grits and, using your hands, shape grits around cheese to form a ball. Repeat with remaining grits and cheese.
Heat oil to 350 degrees F in a large pot fitted with a deep-fry thermometer over medium-high heat. Preheat oven to 250 degrees F. Place flour on a small plate. In batches of 6, roll fritters in flour to lightly coat, then deep-fry until golden brown, 2 to 3 minutes. Transfer fritters to paper towels to drain. Season with salt, then transfer to a sheet pan in oven to keep warm until all batches have been fried.