To a large pot over medium heat, add canola oil, leeks, onion and garlic. Cook for 3 to 4 minutes, stirring often, until softened.
Add salt, parsley, thyme and paprika and cook one minute.
Add potatoes an vegetable broth and bring to a simmer over medium-high heat. Cover, reduce heat to medium, and cook for 8 to 10 minutes or until potatoes are tender.
If desired, use an immersion blender or food processor to puree some or all of the soup for a creamier texture.
Garnish with fresh parsley if desired and serve.