Irish Leek and Potato Soup with Smoked Paprika and Coconut Milk

Heat the olive oil in a large heavy-bottomed pot over medium heat. Add the sliced leeks and cook, stirring occasionally, until they are soft and slightly translucent, about 5-7 minutes. The leeks should be fragrant and beginning to caramelize around the edges.
Add the minced garlic and smoked paprika to the pot. Cook for another minute, stirring constantly, until the garlic is fragrant and the paprika releases a smoky aroma. Be careful not to burn the garlic.
Stir in the diced potatoes and cook for 2-3 minutes, allowing them to absorb the flavors and develop a slight translucency.
Pour in the vegetable broth, bringing the mixture to a gentle simmer. Cover the pot partially and let it cook for about 15-20 minutes, or until the potatoes are tender when pierced with a fork.
Remove the pot from heat and use an immersion blender to blend the soup directly in the pot until it is smooth and velvety. Alternatively, transfer the soup carefully to a blender and blend until silky, then return it to the pot.
Stir in the coconut milk, then season with salt and pepper to taste. Warm the soup gently over low heat, just until heated through, creating a creamy, smoky-scented broth with a smooth texture.
Taste the soup and adjust seasoning as needed, adding more salt, pepper, or smoked paprika for depth.
Serve the soup hot, garnished with a swirl of coconut milk or chopped fresh herbs if desired. The finished dish should be a velvety, pale golden broth with subtle smoky and sweet coconut notes.