Cut the slice of ham into 5mm/¼in dice and chill until needed. To prepare the sprouts, remove any damaged outside leaves, then halve each sprout.
Cook them in a large saucepan of rapidly boiling salted water for a few minutes until tender, but still with the slightest of bites. Drain in a colander.
While the sprouts are cooking, heat a non-stick frying pan and add the sesame seeds.
Cook on a medium heat for just a minute or two to roast the seeds to a golden brown. Remove the seeds from the pan.
Add the sesame oil to the plan, along with the knob of butter, and warm the ham in the bubbling butter and oil, then add the drained sprouts.
Increase the heat and fry for 1-2 minutes, then season with salt and freshly ground black pepper.
To finish, add the roasted sesame seeds, and spoon the sprouts into a vegetable dish.