Rub chicken thighs with 1 tablespoons olive oil and salt, then let sit while you prepare the sauce so that they come close to room temperature.
For sauce, heat olive oil to medium high heat in a small saucepan. Add shallot and salt, cooking for 3-4 minutes until translucent. Stir in mustard, vinegar and preserves. Lightly simmer for 5-6 minutes, until slightly thickened. Stir in basil and turn off heat.
Preheat oven to 400 degrees. Bring remaining 1 tablespoon olive oil to medium high heat in a 12 inch cast-iron skillet. Wait until very hot, then add chicken thighs skin side down. Cook for 3 minutes, then turn heat down to medium and continue to cook for 8 more minutes so that it can “fry” in it’s own fat, until skin is golden brown. Flip and cook for 10 minutes.
Transfer skillet to oven and cook for 8-10 minutes longer, until meat is cooked through and juices run clear. Transfer to a plate, smother with glaze, and let rest for 5 minutes before serving.