Pat chicken dry and season generously with salt and pepper.
Heat olive oil and butter in a cast iron pan or heavy skillet, then sear chicken skin side down until golden brown, 5–7 minutes a side – then remove to a plate.
Add the garlic cloves to the pan, and cook gently 3-4 minutes stirring often, until just golden - but whatever you do, DON'T let them burn.
Pour in the vermouth, scraping the brown bits on the bottom to loosen, let it reduce by half, about 2 minutes.
Now add the chicken stock, thyme, rosemary and put the chicken back in the pan skin side up.
Bring to a simmer, cover and cook on low for 30–35 minutes until chicken is cooked through and tender – 175-180 degrees.
Remove the chicken to a plate, and add the cream and simmer uncovered 3–5 minutes to thicken slightly.
This is the time to check the seasoning and add more salt & pepper if you want.
Now you can either put the chicken back in the pan and spoon a little sauce over each thigh, or plate.
But the real prize will be serving the chicken with crusty bread to smear the soft garlic cloves on.
