Add potatoes, onion, garlic, salt, pepper and water to a pot and bring to boil, once boiling, cover and turn to simmer for about 20 minutes until potatoes very tender.
Meanwhile roast the broccoli. Preheat the oven to 375°F and line a sheet pan with parchment paper. Spread broccoli out and season well with salt and pepper. Bake 15 minutes or until just beginning to see the tips browning. Depending on your oven or the size of your broccoli florets, it may need longer, up to 10-15 more minutes.
After potatoes are tender in soup, whisk in the brown rice flour and nutritional yeast until well mixed. Let it cook about a minute so it thickens up. Add the milk. Stir well, turn off the heat and then use a hand immersion blender to process the soup until it is completely smooth. Turn the heat back on to medium and once it's bubbling, turn down to low and let it cook another 5-10 minutes or until it thickens to desired consistency. Stir often to prevent sticking to the sides and bottom of pan.
Taste and add any additional salt. Add the roasted broccoli and serve. Top with freshly cracked black pepper.
Optional additions: 3 tablespoons of pickle juice gives extra depth to the soup. You can also add 1-2 tablespoons of liquid smoke for a smoky element.