Heat the butter in a medium saucepan over medium heat. Add the shallot and cook, stirring, until tender, 3 to 5 minutes. Add the potato, bay leaf, garlic, thyme, 1/2 teaspoon salt and some pepper and cook, stirring, until the potatoes are well coated, 2 to 3 minutes more. Pour in the broth and bring to a simmer.
Add the sweet potatoes and simmer until the sweet potatoes and potatoes are tender, about 20 minutes, adjusting the heat as needed to maintain a simmer. Remove from the heat, discard the bay leaf and thyme and let cool at least 5 minutes. Carefully puree until smooth with a handheld immersion blender or in 2 to 3 batches in a blender (do not fill the blender more than halfway full per batch).
Stir in the heavy cream and reheat the soup if necessary, adjusting the consistency and seasoning with additional water, salt and pepper.
Serve hot sprinkled with croutons.
When blending hot liquid, first let it cool for five minutes or so, then transfer it to a blender, filling only halfway. Put the lid on, leaving one corner open. Cover the lid with a kitchen towel to catch splatters, and pulse until smooth.
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