Place the beetroot and leaves in a blender or food processor and pulse until finely chopped.
Bring the water and stock to a simmer in a large pot over medium-low heat.
Heat the olive oil in a large saucepan over medium-high heat; cook and stir the onion in the oil until tender, about 3 minutes. Add the rice; cook and stir another 2 minutes. Mix in the beetroot and leaf mixture, cooking another minute. Pour in the stock mixture 1 cup at a time, allowing the liquid to be absorbed before adding each batch, stirring continually; reduce heat to medium and simmer 20 minutes. Stir in the cheddar cheese. Season with salt and pepper. Continue stirring until creamy and thick, about 3 minutes more. Serve with Parmesan cheese.