Pat the chicken thighs dry with paper towels. Sprinkle the chicken with salt and pepper.
Heat 1½ tbsp of olive oil in a large (12 inch) skillet over medium heat. When the oil is hot but not smoking, add chicken, skin side down and cook undisturbed for 15 minutes.
Flip the chicken and cook for another 15 minutes or longer or until the internal temperature reaches 165°F. Transfer the chicken into a plate. Set aside.
Add butter, minced shallots into the pan, cook, stirring occasionally for about 2 minutes.
Add garlic, cook, stirring occasionally for 30 seconds then add dijon mustard, cook, stirring often for about 1 minute.
Add dry white wine, and cook until reduced by more than half, about 4 minutes.As the liquid simmers, scrape up any crispy bits from the bottom of the pan with a wooden spoon or spatula.
Add chicken broth and bring to a boil for about 2 minutes.
Lower the heat, add heavy cream, and tarragon. Cook for 3 minutes or longer, until the sauce starts to thicken, stirring often. If the sauce is too watery to your liking, add a thickening agent by mixing 1 tbsp of softened butter with 1 tbsp of flour into a paste then stir it in the sauce, cook for about 2 minutes. Strring often.Season the sauce with salt and black pepper if necessary.
Return the chicken, skin side up, and any accumulated juices to the skillet and simmer for about 2 minutes or longer, until the sauce has tickened. Turn off the heat.