Combine the onion, white rice, garlic, chicken broth and chipotle puree in a medium saucepan. Bring to a boil on medium-high heat and then cover and reduce to a simmer. Allow to cook on low for 15 to 20 minutes, or until the rice is cooked.
Remove the rice from heat and add the beans, stir to combine. Cover and let sit for 10 minutes or until the beans are heated through.
Spoon the desired amount of mixture onto a tortilla and add avocado, lettuce, tomatoes and mozzarella and wrap. Repeat with the other 3 wraps and serves.