In a large heavy pot over medium-high heat, heat the oil or melt the butter. Reduce to low and cook the leeks until they are tender, about 5 minutes.
Add the potatoes, carrot, asparagus, garlic, and 4 cups of the broth. Bring to a boil. Reduce the heat and simmer, uncovered, for 20 minutes or until the vegetables are tender.
To make the soup in the electric pressure cooker:
Heat the oil in the pot on saute. Add the leeks and cook, stirring, until they are tender, about 5 minutes.
Add the potatoes, carrot, asparagus, garlic, and 4 cups of the broth. Secure the lid and close the pressure valve. Set the machine to 5 minutes manual pressure. At the end of the cooking time, release the pressure carefully and remove the lid.
To blend the soup:
Using an immersion blender, blend the soup until smooth. Alternatively, you can blend the soup in batches in a food processor.
Add more broth, if desired, to achieve your preferred consistency. Season to taste with salt and pepper.
Store the soup in airtight containers in the fridge for up to four days. To freeze, chill the soup thoroughly before transferring the containers to the freezer.
Promptly store leftovers in an airtight container in the refrigerator, for up to 4 days. For longer storage, place chilled containers in the freezer, for up to 2 months. Reheat prior to serving.Nutritional values are approximate and based on 1 cup soup.