Heat the oil in a medium pot over medium heat. Add the onions and bay leaf, sprinkle with salt and cook until tender and translucent. Add the Jerusalem artichokes and potatoes and stir. Add 8 cups water and the thyme bundle, and stir. Bring to a boil, then reduce to a simmer. Cook until the Jerusalem artichokes and potatoes are fork tender, 15 to 20 minutes. Remove the bay leaf and thyme bundle.
In a blender, puree the soup in batches until smooth. Strain through a fine mesh strainer into a new pot. Bring to a boil and reduce to a simmer. Add the cream and season with salt. Serve, garnishing each bowl with a drizzle of extra-virgin olive oil and the thyme leaves.
Cook's Note: When blending hot liquids: Remove liquid from the heat and allow to cool for at least 5 minutes. Transfer liquid to a blender or food processor and fill it no more than halfway. If using a blender, release one corner of the lid. This prevents the vacuum effect that creates heat explosions. Place a towel over the top of the machine, pulse a few times then process on high speed until smooth.