Fill pot with 4 cups of water. Add ½ tablespoon salt and stir to incorporate, then place pot on stovetop over medium-high heat. Add 1 tablespoon butter and bring water to boil.
Once water begins to boil rapidly, add stone-ground grits and stir 30 seconds.
Partially cover pot with lid. Reduce heat to medium and simmer grits 15 minutes, stirring occasionally to prevent sticking. Note: if your stove runs hot, reduce heat to medium-low.
After 15 minutes, uncover pot. Add remaining 3 tablespoons butter and stir to incorporate.
While stirring, add 2 tablespoons room-temperature heavy cream and stir until cream is incorporated. Once incorporated, slowly add remaining cream in 2-tablespoon increments, incorporating each addition of cream fully before adding more.
Stir constantly until grits thicken and begin to "sputter", approximately 15 minutes.
Once grits are ready, remove pot from heat. Taste grits and stir in additional salt if necessary.
Divide grits into serving bowls, then add desired toppings and stir to incorporate. Serve warm.