Combine first 4 ingredients, stirring with a whisk; set aside.
Heat oil in a Dutch oven over medium-high heat. Add onion to pan; sauté 6 minutes. Add rice, ham, and garlic; sauté 2 minutes. Stir in water mixture; bring to a boil. Cover, reduce heat, and simmer 15 minutes. Add peas and greens; cover and cook 5 minutes. Stir rice mixture; cover and cook an additional 5 minutes or until greens and rice are tender.