Heat the olive oil in a large pot over medium heat.
Add the diced onion and sauté for 5 minutes until translucent.
Stir in the minced garlic and cook for an additional minute.
Add the chopped cauliflower and diced potatoes to the pot.
Pour in the vegetable broth and bring to a boil.
Reduce heat and simmer for 20-25 minutes, until cauliflower and potatoes are tender.
Remove from heat and let cool slightly before blending.
Blend until creamy using an immersion blender or a standard blender.
Return to the pot and stir in the milk and dried thyme; season to taste with salt and pepper.
Serve hot, garnished with additional herbs or a drizzle of olive oil if desired.