Heat olive oil in a heavy-bottomed stockpot over medium heat.

Add onion, garlic, carrots, and celery; sauté for 5 minutes until the onion is translucent.

Incorporate the cubed potato, broccoli, and dried thyme, stirring to coat with oil.

Pour in the vegetable broth and increase heat to bring the mixture to a boil.

Reduce heat to low, cover, and simmer for 15 minutes until the potatoes and carrots are fork-tender.

Remove from heat and process the soup using an immersion blender until a uniform, smooth consistency is achieved.

Return to low heat, stir in the heavy cream, and season with salt and pepper.

Warm through for 2 minutes, ensuring the liquid does not reach a secondary boil.