Preheat oven to 375 degrees.
Pat dry chicken pieces and season all over with kosher salt and pepper.
Heat olive oil in a cast iron (or oven-safe) skillet over medium-high heat. When hot, add the chicken skin-side down and cook until golden brown, 3 to 4 minutes per side. Set browned chicken aside on a plate (it doesn't need to be cooked through, as it will finish cooking later).
Discard excess fat from the skillet and reduce the heat to medium. Add the ghee and let melt. Add the shallots and garlic and cook, stirring, until fragrant, about 1 minute, being careful not to burn.
Add grainy mustard and dijon mustard. Stir to combine with shallots and garlic. While whisking, slowly stir in the white wine and bring to a simmer. Let cook, simmering until the white wine has reduced just a bit, about 2 to 3 minutes.
Stir in the chicken broth and whisk until well combined. Nestle the browned chicken pieces into the sauce and sprinkle with the thyme.
Place into oven and bake until chicken is just cooked through, about 10 minutes.
Remove from the oven and stir in the creamer. Place back into the oven and let cook for 5 more minutes, or until the sauce has combined and flavors have melded.