In a saucepan, combine water, half-and-half, salt and white pepper and bring to a boil.
Slowly pour grits into boiling water while whisking the entire time. (Watch out for splattering; mixture is very hot.)
Reduce to low heat and continue to whisk often, until thick and completely smooth, about 10 minutes.
Add cheese and stir gently until cheese melts. Whisk again to combine.
Add cheese and stir gently until cheese melts. Whisk again to combine.
Turn heat off and allow grits {and yourself} to rest 5 minutes. {All that whisking is sure tiring. But worth it. I promise.} Add butter and stir until completely smooth & silky.