Heat oil in a saucepan over medium-high heat. Sauté ginger and 1 cup rice 30 seconds. Stir in 1 cup water, 1/2 teaspoon salt, and 1 cup coconut milk; bring to a boil. Cover, reduce heat, and cook 15 minutes, or until tender. Puree 1 cup coconut milk, 1/2 teaspoon salt, lime juice, spinach, and sugar in a blender. Fold into rice.