In a large stockpot, melt the oil and butter over medium heat. Add onion, garlic, carrot, celery, and fennel (add chopped chard stems, if using.) Sauté until vegetables are tender, about 8 minutes.
Stir in the thyme, rice, stock, salt and pepper. Bring to a boil, partially cover and reduce heat. Simmer for 25 minutes.
Stir in butternut squash, cover slightly and simmer for an additional 25-30 minutes or until squash is tender. Add chopped greens and stir until wilted.
Taste for seasoning and garnish with fennel fronds, if desired. If you like a little acidity, add a few drops of apple cider vinegar. (I think the soup is better with the vinegar.)