Bring 8 cups of vegetable broth to a boil in a large pot. Whisk in the polenta. Reduce heat to low and cook for 30-40 minutes or until the polenta thickens and pulls away from the sides.
Bring a large pot of water to boil. Add the whole rainbow chard leaves and boil until the stems are tender and easily pierced with a fork, about 10-15 minutes. Drain and rinse with cool water. Squeeze any extra water from the leaves and then slice into half inch thick ribbons. Set aside
In a large frying pan over medium head warm a few tablespoons of olive oil and butter. Add the mushrooms and onions to the pan, season with salt and pepper, and saute until the onions are soft and translucent and the mushrooms are tender. Add the sliced rainbow chard to the pan and stir until warmed through and well coated in the pan juices. Stir in the balsamic vinegar and remove the pan from the heat.
When the polenta is finished cooking stir in the cheddar cheese, 1/4 cup butter or olive oil until melted and well combined. Season with salt and pepper to taste.
Spoon the polenta into a bowl, and then top with the sautéed mushroom mixture, and toasted pine nuts. Enjoy!