Add 1 cup water, spinach, onion, cilantro, and garlic to bowl of blender. Puree until mixture is bright green and smooth, about 2 minutes; set aside.
Heat oil in medium saucepan over medium-high heat; add rice. Cook, stirring occasionally, until rice is coated in oil, about 1 minute. Add reserved spinach mixture and chicken bouillon mixture to pot. Stir to distribute rice evenly. Bring liquid to boil. Reduce heat to medium-low. Simmer, covered, until rice is tender and water is absorbed, about 25 minutes.
Remove pot from heat. Gently stir in cheese. Serve warm.