In a medium heavy saucepan, combine the water and milk and bring it to a boil (keep an eye on the pot, as the milk can boil over!). Season the liquid generously with salt, then whisk in the grits. Bring the mixture back to a boil while whisking. Continue whisking for 2-3 minutes, or until the grits are slightly thickened (the mixture will still be quite liquidy, and that’s okay).
Reduce the heat to low and partially cover the saucepan (there should be a small crack so that some steam can escape). Cook, stirring often with a rubber spatula, until the grits are tender and thickened, about 30-40 minutes (they should feel soft on the tongue, not gritty). Feel free to splash in more milk as needed while cooking if the grits start to look really thick—they should be creamy and should swirl easily. Stir in the butter. Season the grits generously with salt (this is key for flavor—you will need more than you think!).
Remove the saucepan from the heat and cover it until you're ready to serve, up to 30 minutes. If you want to hold the grits for longer, drizzle a bit of milk over the surface before covering (this will help prevent a skin from forming)—they can sit out for up to 1 hour. Before serving, reheat the grits over low, stirring and adding more milk if needed.