Sources say to shake and strain into a cocktail glass, but with the small amount of lemon juice, stirring rather than shaking is fine.
No garnish listed, but a lemon twist works well.
There is an earlier cocktail named Boomerang, published by Robert Vermiere in 1922 and by Carlo Beltramo in 1924 in Geneva, but it is an entirely different drink (gin, marashchino, dry and sweet vermouth, no Swedish punsch). 1932's The Green Cocktail Book (London) has a similar variation using equal parts gin, dry and sweet vermouth, a dash of Angostura, with no punsch.
In 1936 Frank Meier's Artistry of Mixing Drinks includes a Boomerang with Angostura and equal parts Scotch, dry vermouth, and punsch.
This is the most common version of the Boomerang, published in the Savoy Cocktail Book in 1930 and both The Cafe Royale Cocktail Book and UK Bartender's Guide in 1937.
Savoy Cocktail Book, 1930; The Cafe Royale Cocktail Book, 1937.