Preheat the oven to 425 degrees F. Season the chicken with paprika, lemon zest, and a pinch each of salt and pepper.
Heat the olive oil in a large skillet/braiser set over medium heat. When the oil shimmers, add the chicken and cook on both sides until golden, about 5 minutes per side. Remove the chicken from the pan.
To the skillet, add the shallots, carrots, and mushrooms. Cook 5 minutes, until just caramelized. Add the butter, wild rice, orzo, garlic, rosemary, thyme, and apple, if using. Cook 5 minutes, until lightly toasted and golden. Add the apple cider, wine, dijon, lemon juice, and ½ cup of water. Season with salt and pepper. Bring to a boil over high heat.
Slide the chicken back into the pan. Add the rosemary sprig. Bake, covered, for 30-40 minutes, until the liquid is absorbed and the rice is cooked. During the last 10-15 minutes of cooking remove the lid and allow the chicken to crisp; if needed, add in ¼ cup additional water or chicken broth to keep the rice from getting dry.
To serve, fluff the rice with a fork and serve the chicken, rice, and veggies together. Enjoy!