Melt butter over medium heat in large saucepan. Add squash, carrots, onions, and celery, saute for 10 minutes. Add chicken broth until vegetables are just covered, bring to a boil.
Cover, reduce heat to simmer for 40 minutes. Remove from heat and place vegetables into a blender (reserve liquid in the pot).
Blend until smooth, return mixture to pot and stir into liquid, add half and half, salt and pepper to taste and any additional chicken stock to get the consistency you desire.
Notes
To blend the soup, you can either use an immersion blender right in the soup pot or transfer it to your blender (love my Ninja) and puree until smooth.