Melt the butter with the olive oil either in a pan or in the microwave
Dry the chicken halves then brush with the melted butter and oil.
Place the chicken pieces, skin side down in a grill pan and cook for about 15 minutes on each side, brushing with the oil and sprinkling with salt twice during the cooking.
Mix the mustard, cayenne pepper, onions and thyme together in a basin, adding 2 tablespoons of the melted fat very slowly, drop by drop.
Spread this mixture all over the chicken pieces.
Roll the chicken pieces in the breadcrumbs, pressing down on them firmly.
Put the chicken pieces back on the grill pan and sprinkle with the remaining fat and grill until crisp and golden - about 10 minutes. Watch they don't burn, turn heat down if they cook too quickly.