Melt the butter in a medium saucepan, over medium heat. Add the onion and garlic and cook until translucent, about 5 minutes. Add the potato, thyme, salt, and broth and bring to a boil. Adjust the heat to maintain a gentle simmer, and cook uncovered until the potato is fork tender, about 10 minutes. Add the broccoli and simmer for 3 minutes.
Puree the soup in batches in a blender or with an immersion blender. Return soup to the pot and add the cream. Bring to a simmer, taste, and season with salt and pepper.
Serve with optional toppings.
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