In a heavy bottomed saucepan, gently bring the milk and salt to a boil. stirring constantly. Whisk the grits into the milk in a steady stream.
Continue to whisk for 1-2 minutes until fully incorporated. Immediately lower the heat to low and cover.
Allow the grits to gently bubble on low heat for 15 minutes stirring periodically to prevent sticking.
Uncover and check the consistency at 15 minutes. Add more milk or water to thin, if needed. Cook for an additional 5-10 minutes. The grits should be thickened and creamy the consistency of porridge.
Add 2 tablespoons of butter and ½ cup cream or half & half at the end of cooking. Stir until the butter has completely melted.
Remove from the heat and mix-in the shredded cheddar cheese, stir until melted.
Serve immediately with additional shredded cheese on top, if desired.