Heat the olive oil in a large stockpot over medium heat. Add the diced onion, carrots, and celery, sautéing for about 5 minutes until soft.

Stir in the minced garlic and dried thyme, cooking for another minute until fragrant.

Add the cubed potato, cauliflower florets, vegetable broth, salt, and black pepper. Bring the mixture to a boil over medium-high heat.

Reduce the heat to low, cover the pot with a lid, and let it simmer for 15 minutes until all vegetables are fork-tender.

Remove from heat. Use an immersion blender to puree the soup until smooth and creamy. Stir in the almond milk if using, taste, and adjust seasoning.