I always thought Carvel was a NY or Northeast thing only. As a kid I loved hokey the commercials with Tom Carvel, the founder and owner of the chain. There are still many around here (NY) , and they are pretty good.
Here is there history...http://www.carvel.com/about_us/history.htm
They used to make the kind of cone you wrote about, chocolate or cherry dipped, at your request, but later started making them ahead and selling them out of a freezer. They called it a Brown Bonnet or a Cherry Bonnet if I recall correctly. To me, once you place soft ice cream in a freezer and store it a while, it loses the properties that make it appealing in the first place.
Now, since we don't have any DQ's in the down-state NY area (or very few) the only option for a fresh made dipped cone is Mr. Softee, http://www.mistersoftee.com/about.asp
who has chocolate dip, cherry dip, and sometimes blue berry dip. If you come to NY we can sit on the front steps of my house and wait for him to drive by. One of the joys of summer!