Peel and dice the potatoes into 1-inch cubes, setting them aside for later.
Heat the large pot over medium heat and add a tablespoon of olive oil until shimmering and fragrant.
Add the diced onion to the pot and sauté for about 5-7 minutes, stirring occasionally, until it turns translucent and begins to smell sweet.
Toss in the minced garlic and cook for another 1-2 minutes, until fragrant and slightly golden.
Add the diced potatoes to the pot and stir to coat them with the onion and garlic mixture. Cook for 2 minutes, allowing the potatoes to start to absorb the flavors.
Pour in the vegetable broth, raising the heat to bring the mixture to a gentle boil, around 200°C (390°F). Reduce the heat to low, cover the pot, and let it simmer for 15-20 minutes, until the potatoes are tender and easily pierced with a fork.
Remove the pot from heat and carefully blend the soup using an immersion blender directly in the pot, or transfer in batches to a blender. Puree until smooth and silky, about 1-2 minutes.
Return the soup to low heat if needed, then season with salt, pepper, and optional smoked paprika or thyme. Taste and adjust the seasoning to your preference.
Finish by drizzling a little extra virgin olive oil over the soup or adding fresh herbs for brightness.
Serve hot, garnished with your favorite toppings like chopped chives or vegan bacon for extra texture and flavor.