Pat the chicken thighs dry, then place in a large ziplock bag. Add the Old Bay Seasoning and the pepper, then seal the bag and shake to coat the chicken with the spices.
In a large skillet over medium-high heat, melt the butter with the vegetable oil. Add the chicken, skin side down. Cook until browned, about 5 minutes.
Flip the chicken over, then add the chicken stock and the lemon juice. Continue to cook until a thermometer inserted in the chicken registers 165ºF, 20-30 minutes.
Remove the chicken to a plate. Turn the heat down to low and add the creme fraiche and basil. Allow the sauce to heat through, about 2 minutes. Add the chicken back to the pan and spoon the sauce over. Sprinkle with additional basil and serve.
