Oil a medium sheet pan. In a saucepan bring water and butter, seasoned with salt and pepper, to a boil. Reduce heat to medium and whisk in grits. Cook, stirring frequently, until the grits are tender, 20 to 25 minutes, adding more water if the grits become too thick while simmering.

Remove from heat and stir in cheese. Pour grits onto sheet pan, spreading them evenly. Cool and cut into cakes with a 2 1/2- to 3-inch biscuit cutter.

In a large nonstick skillet, heat enough oil to coat bottom of pan over medium-high heat. Dredge both sides of cakes in flour and pan-fry about 2 minutes on each side, until golden. Drain on paper towels and keep warm before serving.