Cut off the dark green leaves and the very bottoms by the roots. (Discard the dark green leaves or save it for making homemade stock.)
Cut the white stalks in half, length-wise. Rinse off each half under some cold running water. Make sure to get in between the layers because dirt likes to hide there. Shake the water off very well and the halves are not ready to slice.
Potato Leek Soup:
Slice each leek half into thinly, width-wise. Wash and slice celery ribs as well. Peel or wash potatoes and cut them into cubes.
Preheat the pot over medium heat and melt butter. Saute leeks in butter until soft. Add celery and saute it until leeks start to get some sear.
Add potatoes and saute for a couple more minutes.
Add bay leaf and thyme sprigs to the pot and pour in chicken stock. Pour in enough chicken stock just to cover the potatoes. (Too much stock will result in a thin soup.)
Season with salt and pepper, stir well, cover the pot with a lid, and cook until potatoes are tender.
Take out the bay leaf and thyme sprigs.
Stir in heavy whipping cream until completely incorporated.
You can transfer the soup into a blender or use an immersion blender to blend the soup. Blend it until smooth.