In a saucepan, melt the butter and saute the ginger until it's sizzling.
Add the carrots and stir-fry them for about 3 minutes.
Pour in the broth and simmer uncovered until the carrots are quite tender, 10 to 15 minutes.
In a food processor or blender, puree the soup in 2 or more batches (hot foods expand when beaten).
The recipe may be prepared to this point and refrigerated for later use.
Whisk in the milk and reheat the soup, but don't boil it or it will separate.