In a Dutch oven or large pot, heat the butter over medium-high heat until melted. Add in the onions and cook until translucent. Continue stirring the butter until golden brown bits form. Add the squash and stir to coat for about 5 minutes.
Add 6 cups of broth and bring to a boil. Lower the heat to simmer and cover for 10 – 15 minutes, until the squash is fork tender.
Working in small batches, transfer the soup to a blender and blend until smooth. Do not fill the blender more than half way each time and transfer to a temporary pot. Once the entire batch has been blended, transfer back to the Dutch oven over medium-high heat. If the soup is too thick, add the last cup of broth, as necessary, ¼ cup at a time.
Stir in the cream, brown sugar, and nutmeg. Bring back to a boil and simmer uncovered until slightly thickened. Add salt to taste.