Start by heating the olive oil in a heavy-bottomed pot over medium heat. Add the chopped onion and cook, stirring occasionally, until it becomes translucent and fragrant, about 5 minutes.
Add the minced garlic to the pot and cook for another minute, until it releases a warm aroma and slightly darkens at the edges.
Stir in the diced potatoes, coating them with the aromatic mixture, and cook for 3-4 minutes until they start to soften and turn slightly translucent around the edges.
Pour in the vegetable broth, ensuring the potatoes are fully submerged. Bring the mixture to a gentle simmer, then cover and cook for 15-20 minutes, or until the potatoes are very tender and easily pierced with a fork.
Once the potatoes are soft, remove the pot from heat. Use an immersion blender to carefully blend the soup directly in the pot until smooth and velvety. Alternatively, transfer the soup in batches to a blender, blending until smooth, then return to the pot.
Taste the soup and season with salt, pepper, and optional smoked paprika or fresh herbs for added flavor. Stir well to incorporate the seasonings evenly.
Let the soup sit for a few minutes off the heat to thicken slightly and allow the flavors to meld, then ladle into bowls.
Finish with a drizzle of olive oil or a sprinkle of chopped herbs for a fresh touch.