Heat all of the gooseberry jam ingredients apart from the wine in a heavy-based saucepan over a medium heat until the sugar has dissolved and the gooseberries have started to break down (approximately 15 minutes).
Pour in the white wine and bring the to the boil, scraping up any burned bits from the bottom of the pan using a wooden spoon. Continue to simmer until most of the wine has evaporated and the mixture had thickened slightly. Set aside for a few minutes to cool slightly.
Strain the jam mixture through a fine sieve, collecting the strained liquid in a clean saucepan. Reserve the strained pulp.
Bring the strained liquid to the boil, then reduce the heat until the liquid is simmering. Continue to simmer until the volume of liquid has reduced by half and thickened.
Transfer the strained pulp to the bowl of a food processor and blend until smooth. Add the reduced liquid to the jam as necessary, blending to combine, until the consistency of the jam is to your liking (you may not need all of the reduced liquid).
For the duck, heat a large griddle pan over a high heat. Score the skin of each duck breast in a criss-cross pattern using a sharp knife.
When the pan is smoking, add the duck breasts, skin-side down, and cook for 4-5 minutes, or until the fat is crisp on the outside and has started to melt.
Turn the duck breasts over and fry for a further 3-4 minutes, or until the meat has browned on the outside but is still pink in the centre. Remove from the pan and set aside on a warm plate to rest for five minutes.
While the duck is resting, blanch the broccoli in a large pan of salted water for 1-2 minutes, or until just tender. Drain well.
To serve, carve each duck breast into thick slices and arrange each on a serving plate. Spoon a dollop of the gooseberry jam on top. Serve the broccoli alongside.