The "toasted on the dry side" version seems to come only from the 1920s.

In the '30s, in my Grandparents' house where I lived, we did not have a toaster. My grandmother would make toast under the broiler of the oven, one-sided. But not toasted "on the dry side", and not as a means of avoiding wastage of already-buttered bread.

Instead, the procedure was to butter the pieces of bread and then
toast them in the broiler, buttered side up. The resultant toast was spotty, sort of like a palomino horse.

Dave Oesterreich