For the sauce, fry the shallot in the oil for 5 mins or until softened but not coloured. Add the plums and sugar, stirring for a few mins until the sugar has dissolved. Add the red wine and stock, then simmer for about 15 mins, stirring occasionally, until softened and slightly thickened. Keep warm or leave at room temperature for up to a day before reheating to serve.
Meanwhile, heat the oven to 180C/ 160C fan/gas 4. Score the skin of the duck breasts with a sharp knife and season well with salt and pepper. Heat a non-stick frying pan and place the duck breasts in, skin-side down. Fry for 6-7 mins, then turn and add the thyme, star anise and butter. Allow this to melt, basting the duck with the juices, then transfer everything to a small roasting tin and finish in the oven for 5-6 mins for pink or 10-12 mins for well done.
When the duck is ready, baste again with the juices, then rest for 5 mins while you finish everything else.