Peel and dice the potatoes into roughly 2 cm cubes, ensuring they are uniform for even cooking.
Heat the olive oil in a large pot over medium heat until it shimmers and starts to smell fragrant. Add the chopped onion and sauté until it becomes translucent and fragrant, about 5 minutes.
Add the minced garlic to the pot and cook for another minute until fragrant, stirring constantly to prevent burning.
Pour in the diced potatoes and vegetable broth, ensuring the potatoes are covered by about an inch of liquid. Increase the heat to bring the mixture to a gentle boil.
Reduce the heat to low and simmer until the potatoes are fork-tender, about 15 minutes. The potatoes should be soft and breaking apart easily.
Use an immersion blender directly in the pot or carefully transfer the mixture in batches to a blender. Blend until smooth and velvety, with no lumps remaining, about 1-2 minutes.
Stir in the nutritional yeast (if using), season with salt and pepper to taste, and reheat gently for 2 minutes if needed.
Serve hot, garnished with fresh herbs and an optional drizzle of olive oil or a sprinkle of additional nutritional yeast. Enjoy the creamy, comforting bowl of vegan potato soup.