Heat 2 Tbsp. olive oil in a large skillet over medium high heat. Season chicken with salt and pepper, add to skillet and cook until well browned and pieces release easy from the pan (approx.5-6 min.). Turn chicken over and repeat until all sides are browned. Chicken will be seared but not cooked at this point. Remove from skillet, set aside.
Reduce heat to medium, add mushrooms and cook until browned on both sides (you may need to add a little more olive oil) Remove from skillet, set aside.
While chicken is cooking, cut Asparagus stalks into 1 inch pieces. Cut ½ of a lemon into thin slices. Set aside.
Add shallots to skillet and cook until soft (2-3 min.) Add garlic and cook until aromatic (about 1 min). Add rice and chicken stock, and wine (if using); bring to a boil. Reduce heat so that rice is just gently simmering. Stir in mushrooms.
Arrange chicken, lemon slices, asparagus and rosemary on top of rice. Cover the skillet and cook undisturbed for 15-20 min. You want the liquid to be fully absorbed, the rice tender and the chicken fully cooked. If necessary add additional chicken stock (or water) to the rice and continue cooking if chicken is not fully cooked (155-165F with a thermometer). Squeeze the juice of remaining ½ lemon over the chicken and rice; serve on individual plates or a serving platter.