Remove the chicken from the refrigerator and place it on a plate or tray. Season with salt and pepper and let come to room temperature while you prepare the glaze.
In a large, deep skillet, heat 1 tablespoon olive oil over medium-high heat. Add the shallot and sauté until fragrant and beginning to brown, about 2 minutes. Add the cranberries, water, cider vinegar, and honey. Cook until the berries soften and begin to lose their shape, 5-8 minutes. Stir often so that the berries cook on all sides and much of the liquid cooks away.
Once soft, roughly smash the berries with the back of a wooden spoon so that they burst, then stir in the ginger, salt, and allspice. The mixture will be very thick. Transfer the cranberry glaze to a bowl.
With a paper towel, carefully wipe the skillet clean, then heat the remaining 1 tablespoon olive oil over medium-high heat. Once hot and shimmering, add the chicken thighs in a single layer, seasoning-side down. Let the chicken cook for 5-7 minutes undisturbed, until the first side is golden brown and does not stick to the pan. For the best browning, try not to move the chicken around in the pan as it cooks. Flip the chicken over, then cook it an additional 4-6 minutes, until the juices run clear and a meat thermometer inserted in the center reads 165 degrees F.
Transfer the chicken to a serving plate and spoon the cranberry glaze over the top. Let rest 5 minutes, sprinkle with chopped fresh thyme, and serve with extra cranberry glaze for dipping.
TO STORE: Leftovers may be stored in an airtight container in the refrigerator for up to 3 days.
TO FREEZE: Freeze the chicken and cranberry sauce in a freezer-safe container for up to 3 months. Defrost overnight in the fridge before warming.
TO REHEAT: Warm in the microwave, in a covered skillet over medium-low heat, or in a slow cooker until heated through. You may need to add a few tablespoons of water to the sauce to rehydrate it before heating.