Melt the butter over medium heat in a stock pot. Add the leeks and garlic and cook, stirring occasionally, until vegetables are softened (~10 minutes).
Add potatoes, broth, bay leaves, thyme, salt and pepper; bring to a bubbly boil; cover and reduce heat to low; simmer ~15 minutes, until potatoes are tender.
Remove thyme sprig and bay leaf; transfer all to a blender; purée.
Return all to stock pot; stir in heavy cream; heat through.