Rinse the Grains: Place the barley grits in a fine-mesh sieve and rinse thoroughly with cold water to remove excess starch. Drain well.
Start the Pot: In a deep pot, bring the 4 cups of water to a boil. Add the olive oil, salt, cumin, and the rinsed barley. Stir well to prevent sticking.
Simmer: Lower the heat to medium-low. Cover the pot partially (leave a small gap for steam to escape) and simmer for about 15 minutes. Stir occasionally until the barley is soft and the mixture has thickened.
Add Creaminess: Pour in the milk or extra water if needed for vegan. Stir and let it simmer for another 2–3 minutes until heated through and creamy.
Serve: Ladle into bowls and drizzle generously with extra virgin olive oil. Serve hot with sweet dates.