In the saucepan, stir together the water, milk, sugar, and kosher salt and bring to a boil. Reduce heat to low and slowly add the grits, gently whisking until all the grains are added. Cover and bring back to a boil. Uncover and reduce heat to medium –low and allow to simmer, stirring occasionally until the grits have thickened, about 1-½ hours. Add a little more milk if the grits are too thick. Stir in 1 tablespoon of butter.
Start the bananas when the grits are almost done. Melt 1 tablespoon of butter in the nonstick skillet, then stir in the brown sugar and nutmeg. Add the sliced bananas and cook until the bananas are soft, about 3 minutes.
Serve grits in small bowls topped with bananas and warm maple syrup.