Add the water and salt to a medium sauce pot. Place a lid on top, turn the heat on to high, and bring the water up to a rolling boil. Once boiling, stir in the grits. Turn the heat down to low, replace the lid, and let simmer for 5-7 minutes, or until thickened.
Add the butter and milk to the grits and stir until the butter has melted and the grits are smooth. Stir in the grated cheddar, one handful at a time, until fully melted in and smooth. Leave the lid on the pot with the burner turned off to keep the grits warm.
Cook four eggs using your favorite method (fried, scrambled, soft boiled, etc.). Slice the green onions.
To build the bowls, place one cup of the cheddar grits in a bowl, top with one egg, 1/4 cup salsa, some freshly cracked pepper, and a sprinkle of sliced green onions.