Heat olive oil in a large pot over medium heat. Add leeks and onion, sauté for ~8 minutes until softened.
Add garlic, cook 1 more minute. Mix in smoked paprika, thyme, and potatoes. Add vegetable broth and beans, cover, and simmer 12–15 minutes until potatoes are tender.
Remove lid and use a stick blender to blend about half of the soup for a creamy texture.
Add cavolo nero and soy milk, cook for 5–6 more minutes.
Meanwhile, heat olive oil in a pan, add bread cubes, and cook until golden and crispy. Season with salt and pepper.
Turn off heat for the soup, stir in nutritional yeast, lemon juice, and adjust seasoning with salt and pepper.
Serve hot, topped with croutons, parsley, black pepper, and a drizzle of olive oil.