Melt the butter in a large heavy-based pot. Add the celery, onion, leeks & bay leaves with a good pinch of salt. Cook gently for 10 minutes until softened and fragrant.
Stir in the garlic and cook for another 2 minutes.
Add the potatoes and pour over the stock. Bring to the boil, then reduce to a simmer. Cook uncovered for 25–30 minutes, or until the potatoes are tender and starting to fall apart.
Use a potato masher or the back of a spoon to crush some of the potatoes in the pot, this thickens the soup while keeping it nice and chunky. Or you can use a hand blender and blend half of the mixture.
Stir in the milk and cream, taste, and season generously with salt and black pepper.
Ladle into bowls and scatter with fresh chives to finish.
