Put the cottage cheese in a sieve over a large bowl and press the mixture through the sieve with the back of a spoon. Set aside.
Process the chorizo and onion in a food processor until finely chopped. Add the chicken and oregano, season with salt and pepper and process until mixed. Tip into the cheese and mix well until evenly combined. (This is best done with your hands.)
Divide the mixture into 4 even-sized pieces and shape each one into a burger. Chill for at least 1 hour.
Place the burgers in a lightly oiled shallow roasting tin on the upper rack of the halogen oven. Set the temperature to 200°C (392°F) and cook the burgers for 12 minutes, turning them once, until cooked through. Serve in burger buns with a leafy green salad and spicy relish.