Preheat oven to 200°.
In a bowl, coat chicken with olive oil, thyme, salt and pepper. Heat a little more oil in a heavy ovenproof frying pan, and sear chicken, skin side down, in the frying pan until skin is crisp and golden. Reduce heat a little, and fry on medium heat for 6-8 minutes, turning once. When both sides are golden, transfer pan to the lower shelf of the hot oven for 10 minutes. Remove pan and allow chicken to rest for 5 minutes.
While the chicken is frying, wipe mushrooms and place gills-side up in a baking tray. Drizzle with white wine vinegar and oil, and place dabs of butter on each mushroom. Top with sage leaves and season with salt and pepper. Bake on the top shelf at 200 degrees for 15 minutes.
To make blue cheese sauce, melt 10g of butter in a saucepan on low to medium heat, and add cream. Once butter has melted into cream (but not boiled) add small chunks Puhoi Valley Kawau Blue and a little cracked pepper, and simmer until sauce has thickened.
Serve chicken breast with sage mushrooms and a generous helping of blue cheese sauce. Serve with a fresh green salad or seasonal greens.