Peel onions, garlic and squash and roughly chop. Chop leeks and wash thoroughly.
Melt butter in Dutch oven (or large saucepan) over medium heat. Add onions, garlic, leeks and squash. Season with salt and pepper. Gently sauté for 2 – 3 minutes.
Add half the ale and cover for 5 minutes. Add the stock and bring to a boil.
Pick basil leaves, wash and pat dry with a cloth. Tie with string, bruise slightly with a mortar and pestle and add to soup. (*See note)
Simmer soup until squash is soft, remove basil stems and puree with an immersion blender (or carefully in batches in a blender).
Add the rest of the ale and most of the cheese. Season with salt and pepper. Stir to combine.
Chiffonade basil. Serve soup and garnish with remaining cheese and basil.
*If you don't have a mortar and pestle, place basil in a plastic bag and using a rolling pin, or similar heavy kitchen utensil, pound the basil to bruise it.