Pour the chicken stock into a large sauce pan or stock pot. Add the peeled squash.
Cover and cook the squash on medium heat, turning occasionally with a spoon, until it is soft and tender.
Remove the cover and continue to cook briefly until most of the moisture has evaporated.
While the squash is cooking, pour the whipping cream into a 1-qt. sauce pan.
Add the thyme leaves and heat the cream over a very low heat to infuse the cream with the thyme.
When the squash is soft and dry, turn off the heat. Add the infused cream and mash with a potato masher.
Add the butter; season to taste and serve.