In a large pot over high heat, combine vegetable stock, chopped potatoes, and dairy-free butter. Bring to a boil and cook for about 5 minutes.

Once the potatoes are partially tender, add broccoli florets. Lower the heat to medium and boil uncovered for another 5 minutes.

Remove pot from heat and let cool for 5 minutes. Blend half of the mixture until completely smooth.

Pour the blended soup back into the pot, adjust the consistency with more stock if needed, season with salt and pepper, and serve warm.