Measure the boiling water in a large glass measuring cup or large mug. Place the yerba mate tea leaves in a tea ball or a tea bag and place in the boiling water, allow to steep for 5 minutes, remove the tea ball and set the brewed tea aside.
In a large stock pot, warm the oil. Saute the onion and carrot until tender and translucent. Add the garlic and sauté until fragrant, about 1 minute.
Add brewed Yerba Mate, chicken stock, salt, rice, and potato and bring to a boil. Lower heat to a simmer and cook, covered until potatoes and rice are tender, about 15 minutes.
Meanwhile, process cilantro and water in a blender. Stir into the soup mixture along with the cooked chicken and frozen vegetables and cook until heated through, about 5 minutes.
Taste for salt and pepper and serve with wedges of lime.