According to this 1971 advertisement, Athole is a small town in Scotland. And Brose is the Scottish word for brew.
Athol Brose is something like egg nog without the eggs.
1971 recipe from old Dewar's advertising
1 cup honey (heather honey from Scotland, if you want to be 100% authentic
1 1/2 to 2 cups heavy sweet cream
2 cups Dewar's White Label Scotch Whisky
Heat honey and, when it thins slightly, stir in the cream. Heat together, but do not boil. Remove from heat and slowly stir in the whisky. It may be served hot or cold. Makes 4 to 6 servings.
For complete authenticity, soak 1 cup of oatmeal (not the instant kind) in two cups of water overnight. Strain and mix the liquid with the other ingredients. (Still want to be 100% authentic?)
"No, Grandma, I swear Athole is not a cuss word!"
Recipe via Maria