Heat the olive oil in a large pot over medium heat until shimmering and fragrant.
Add the diced onion and sauté, stirring occasionally, until translucent and fragrant, about 5 minutes. You should see the onions turn soft and slightly golden.
Add the minced garlic and cook for another 30 seconds until fragrant, being careful not to burn it.
Stir in the chopped potatoes and cook for a couple of minutes, allowing them to begin releasing their starch and develop a slight sheen.
Pour in the vegetable broth, ensuring the potatoes are mostly submerged, and bring the mixture to a gentle simmer.
Cover the pot and let the potatoes simmer for about 20 minutes, or until they are tender and easily pierced with a fork.
Use an immersion blender to carefully blend the soup directly in the pot until it’s smooth and velvety, or transfer in batches to a blender and puree until creamy.
Stir in the plant-based milk and smoked paprika, then season with salt and pepper to taste. Warm the soup gently over low heat for about 5 minutes, stirring occasionally.
Taste the soup and adjust seasoning, adding more smoked paprika for smokiness or a squeeze of lemon for brightness if desired.
Serve the hot, creamy soup garnished with fresh herbs or a drizzle of olive oil for extra flavor.