Heat gooseberries, sugar, elderflower, star anise, and cinnamon in a saucepan until sugar dissolves.
Add 20ml white wine, bring to a boil, and simmer until liquid reduces and thickens.
Strain the mixture through a fine sieve to separate the liquid from the pulp.
Boil the strained liquid separately until reduced by half.
Blend the pulp in a food processor, adding reduced liquid until the desired consistency is reached.
Score the skin of the duck breasts in a criss-cross pattern.
Sear duck breasts skin-side down in a hot griddle pan for 5 minutes until crisp.
Flip the duck and cook for 4 minutes until browned but pink in the center.
Rest the meat for five minutes and blanch broccoli in salted water for 2 minutes.
Slice the duck and serve with a dollop of jam and the broccoli.