In a large pot, heat the vegan butter or olive oil on medium-high.
(Optional) Sprinkle in red pepper flakes if using, and allow to bloom for a minute.
Add diced onions and sauté until translucent for about 2-3 minutes.
Add in garlic and sauté for another minute.
Add in vegetable broth, cubed potatoes, and bay leaf. Bring to a boil, and then reduce heat to low or medium-low to simmer. Simmer for 10-12 minutes, or until the potatoes are easy to pierce with a fork.
Scoop half of the cooked potatoes out of the soup and into a high-powered blender. (Some of the onions will wind up in there, and that's okay.)
Before blending the potatoes, add broccoli, carrots, spices (onion powder, garlic powder, smoked paprika), and nutritional yeast into the broth. Stir to mix and bring the mixture up to a simmer. Let it simmer over low/medium-low for about 5 minutes while you blend the potatoes and cashews.
Add the soaked cashews into the blender with the potatoes, along with 1/2 cup water, and blend until completely smooth. Add extra water as needed to blend smoothly into a thick creamy consistency. (The exact amount you need will depend on how starchy your potato is. Russets will take a little more water than gold potatoes.)
Pour the creamed potato and cashew mixture into the pot of soup and stir to mix.
Add in the fresh lemon juice and plant-based shredded cheddar cheese.
Cook for an additional 3-5 minutes, until warmed through and slightly thickened.
Taste and add salt and pepper to your taste preference.
Serve in your favorite soup bowl or a bread bowl if you're feeling fancy!