Combine water and milk in a large heavy saucepan. Bring to a gentle boil over medium-high heat. Slowly add grits, whisking constantly. Season with salt and white pepper. Reduce heat to low and simmer, stirring often, until grits are creamy and thick, 45 to 60 minutes.
Taste grits and adjust seasoning. Add sweet potato. Add ground ginger, cinnamon, nutmeg, sugar and butter. Taste and adjust seasonings with salt and white pepper. Serve immediately.