Pat dry chicken thighs.
Combine the tapioca flour, mustard, salt, and pepper in a shallow dish.
Coat chicken in the mixture and set aside, reserve any extra flour mixture.
Heat the olive oil and ½ tablespoon of the butter in a large skillet over medium-high heat.
Once hot, add the chicken to the pan with the skin side down and cook for about 5 minutes until the skin is golden brown and crispy. Flip chicken and cook for another 5 minutes until chicken is cooked through to 165°F. Transfer chicken to a plate and cover.
Drain or wipe out the skillet, reduce heat to medium and add the remaining 1 tablespoon of butter to the pan. Add the chicken broth and goat cheese to the melted butter; whisk together until the goat cheese melts and is incorporated. If desired, add a little bit of the reserved tapioca flour mixture to the pan to thicken the sauce; whisking constantly. Add the tarragon leaves and stir to incorporate.
Return the chicken to the skillet and coat in the sauce.
Serve over rice and top with the cherry sauce.