Preheat the oven to 180°C.
Blend turkey, Brussels sprouts, and one egg in a food processor.
Season the mixture with salt and black pepper.
Shape the mixture into four patties using floured hands.
Heat 25g butter and 15ml oil in a frying pan over medium heat.
Fry burgers for one minute on each side.
Bake burgers on a sheet for five minutes until cooked through.
Simmer relish ingredients in a small pan for eight minutes until cranberries soften.
Add vinegar to a pan of simmering salted water.
Crack two eggs carefully into the simmering water.
Cover and cook for two minutes.
Drain eggs on kitchen paper using a slotted spoon.
Serve two burgers per plate topped with a poached egg and relish.