Heat the oil in a large pot set over medium heat; add the leeks and cook, stirring occasionally, until softened. Add the celery, asparagus and celery root. Cook gently for about 10 minutes or just until softened.

Add the stock and enough water to cover the vegetables. Season with salt and pepper. Bring to a boil.

Purée with an immersion blender. If you are making this ahead of time, freeze or refrigerate the soup at this point.

Bring the soup to a boil and add the oats and thyme. Cook over medium heat for 10 minutes. Purée again with an immersion blender to break up any lumps. Adjust the seasoning and serve with croutons.

Lower the heat to medium-low; cook for 45 minutes or until the vegetables are very soft.

Heat the oil in a large skillet set over medium-high heat. Add the thyme and garlic and sauté for three minutes. Add the bread cubes and brown on all sides. Let cool and add to the soup right before serving.