Start by melting the butter in a medium to large pot, over medium-high heat.
Add the chopped onion and saute until they soften.
Add the all-spice powder and saute for a few minutes, stirring often to avoid burning the spice. (NOTE: Do not hesitate to lower the heat.) Add the bay leaf, potato, and celery, as well as the leaves.
Mix for a couple of minutes to coat everything with the melted butter --- then add a bit of salt.
Reduce the heat to medium-low, cover it with a lid, and let it cook for twenty minutes.
Pour the stock and add the bay leaf; then place the lid back on, and turn the heat up.
Bring to a boil, lower heat, then simmer for fifteen to twenty minutes.
Take the pan out of the heat and remove the bay leaf.
Use an immersion blender to puree the celery soup.
Place it back on the stove, and season with salt and ground white pepper.
Pour the cream, mix, and heat for a few more minutes --- taste and adjust seasoning, if needed.
Transfer your English celery soup into bowls and serve!