Add the onion and carrots to a large pot with a tablespoon or two of water. Sauté until slightly softened, about 2 minutes.
Add the potatoes, beans, broth, nutritional yeast, thyme and garlic powder to the pot and bring to a boil over high heat.
Reduce heat and simmer until the potatoes are easily pierced with a fork, about 8 minutes. Then add the broccoli and simmer 5 more minutes.
Turn off the heat and using a slotted spoon, remove and set aside about 2 cups of the veggies.
Purée the remaining soup in the pot, using an immersion blender.
Return the reserved veggies to the pot, stir in the plant milk and taste for salt. I add 1/2 a teaspoon at this point, but salt to your taste.