Heat a large skillet over medium-high heat. Add the oil and butter. Pat the chicken dry with paper towels.
When the butter is melted add the chicken parts skin side down and brown for 5 minutes; turn and brown the other side for 5 minutes.
Turn the chicken skin side up again, reduce heat to medium, sprinkle with the salt, pepper and the pinch of herb you are using. Cover and simmer for another 5 minutes; turn the chicken, cover and cook an additional 5 minutes.
Check chicken for doneness. If juice is still pink, cover and cook another 5 minutes.
Remove chicken from the pan, cover and keep warm. Do not drain or wipe out the pan.
Keeping the skillet over medium heat, add the onion/green onion. Cook for 1 minute.
Add the wine/vermouth and scrape up the bits at the bottom (deglazing). Add the stock and boil for about 5 minutes until the sauce is reduced and slightly syrupy.
If you want a thicker sauce, use the beurre manie. If not, add the butter, stir and pour over the chicken.
Beurre manie is equal portions of soft unsalted butter mixed with equal portions of flour to form a smooth paste