Prepare the leeks by cutting off any tough green tops and the root ends. Slit the leek vertically through the green end and down an inch or two into the white end. Clean under running water, fanning the layers to get all the dirt and sand out. Slice the leeks into thin rounds.
Melt the butter in a large Dutch oven or similar sturdy pot on medium heat. Add the leeks, chopped onion, sliced carrots, pressed garlic and bacon. Cook on medium heat, stirring occasionally, for ten minutes. Stir in the thyme and pepper and then the peas. Stir to coat the peas and mix everything evenly.
Add the stock or water and bring to a boil. Turn the heat down so the pot is just simmering and cook for 30 to 40 minutes or until all the vegetables are quite tender. Let soup cool a little before processing in blender.
Working in small batches, process the soup in a blender until it is smooth, pouring the blended soup into a different pot as you go. Stir in the heavy cream, season to taste with salt and pepper, and return soup to heat to warm through.
To serve you can drizzle a little cream in a pretty pattern on top of the soup or try it with croutons.