In a saute pan, heat the olive oil on medium high. Then add the onion and garlic. Saute on medium high for 4-5 minutes until the onion is translucent. Remove from heat and set aside.
Now in a large soup pot, melt the vegan butter on low and then add in the flour. Whisk together to make a roux. Cook on low for 1-2 minutes until it is thick and bubbly.
Now whisk in the vegetable broth, until the roux is fully incorporated. Raise the heat to medium high and bring the broth to a simmer. Once it has started to thicken, 3-5 minutes, reduce to low.
Now add the broccoli, carrots and the sauteed onion and garlic, cook for about 2 minutes, then add the soy milk, vegan cheese, nutritional yeast and seasonings. Start with a few pinches of salt and pepper.
Now bring the soup back up to a simmer. Simmer until the vegan cheese has melted and the soup has thickened. 5-10 minutes. Stirring frequently. Now taste and adjust seasoning. I added a lot of salt and pepper, but it is to your preference.
Serve immediately! I like to garnish with green onions.