In a large pot or dutch oven, heat olive oil over medium heat. Cook onion and garlic for 2-3 minutes.
Add butternut squash to pot and cook for 5 minutes. Add broccoli, salt, thyme, and white pepper. Cook covered for an additional 8-10 minutes until tender.
Add vegetable stock and bring to a low simmer. Using an immersion blender, blend vegetables until smooth. Add more vegetable stock as needed until desired thickness is reached.