Set a large pot over medium heat and add the butter. When the butter is melted, add the onion. Saute onions for 2-3 minutes, stirring frequently until softened. Add the garlic and continue cooking for an additional 30 seconds.
Whisk in the flour, thyme, black pepper, and salt. Gradually pour in the milk, whisking continuously until the consistency is smooth.
Add the vegan chicken broth. Bring the soup just to a boil then reduce the heat to low. Add the broccoli and carrots, cover, and simmer for 5 minutes, until the veggies are crisp-tender.
Remove from heat and stir in the cheese. Give the cheese a few minutes to melt then ladle the soup into bowls and serve hot. (For an extra creamy texture, use an immersion blender right in the pot or transfer the soup to a high speed blender to puree until smooth.)