Not sure why this is called a Boston cocktail. There are certainly more famous drinks that have their origins in Beantown. Perhaps this is one of the original Mr. Boston creations from 1933. It does appear in the first edition. As well, it has the flavor profile of a post-prohibition drink. Plenty of fruit flavor to cover up the taste of badly made alcohol.
I thought this was a bit too apricot heavy. I’d cut back the brandy to 1/2 ounce.
0.75oz apricot flavored brandy
0.5oz lemon juice
Shake with ice and strain into chilled cocktail glass.