Peel and chop the potatoes into 2 cm chunks, setting them aside.
Dice the onion and mince the garlic cloves, preparing aromatic base ingredients.
Heat olive oil in a large pot over medium heat until it shimmers and begins to smell fragrant.
Add the diced onion and minced garlic to the pot, cooking gently until they turn translucent and fragrant, about 3 minutes. The onions should be soft and slightly golden.
Stir in the chopped potatoes, coating them with the fragrant onion and garlic mixture, and cook for another minute.
Pour in the vegetable broth, ensuring the potatoes are fully submerged, then bring to a gentle boil.
Reduce heat to a simmer and cook uncovered for about 20 minutes, or until the potatoes are tender and easily pierced with a fork. The broth should be bubbling gently.
Use an immersion blender directly in the pot to puree the soup until smooth and velvety. If you prefer a chunkier texture, mash some potatoes with a fork instead.
Taste the soup and season with salt and pepper, adjusting to your preference. For added warmth, stir in a pinch of smoked paprika if desired.
Let the soup rest for a few minutes to allow flavors to meld, then serve hot, garnished with fresh herbs if you'd like.