In a dutch oven, melt the butter in the olive oil over medium heat.
Season the chicken thighs with one teaspoon salt and pepper to taste. When the butter is melted, add the chicken skin side down to the pan.
Cook the chicken until the skin is golden brown and it releases easily from the pan, about six minutes. Turn the chicken over and cook until the other side is browned, five minutes more. Transfer the chicken to the plate.
Reduce the heat to medium-low and add the thyme leaves to the pan.
When they start to sizzle, add the shallots and the remaining 1/2 teaspoons salt.
Cook, stirring often, until the shallots soften, three to four minutes.
Add the garlic and cook another minute.
Stir in the olives and almonds.
Increase the heat to medium and add the wine, stirring and scraping up the browned bits from the bottom of the pan.
When the wine comes to a simmer, return the chicken to the pan skin side up along with any accumulated juices, then pour in two cups of the chicken broth. Increase the heat to high and bring the broth to a boil.
Reduce the heat to medium-low and simmer, uncovered, until the chicken is cooked through and the sauce thinly coats the back of spoon about 15 minutes. Check on the chicken after eight minutes and if the pan looks dry, add the remaining 1/2 cup broth.
Serve the chicken with a ladle of the sauce with olives and almonds and shower of fresh parsley.