1 Whisk together the sauce: In a mixing bowl or large liquid measuring cup, whisk together the sherry, chicken broth, sour cream, cream, Italian seasoning, salt, pepper, and paprika. Set aside.
2 Cook the onions, mushrooms, and garlic in the pressure cooker: Select the “Sauté” setting on the pressure cooker and heat the oil in the pressure cooker. (If you are using a stovetop pressure cooker, heat the oil over medium heat.)
Add the onion and cook for 4 minutes, until a bit softened but not browned. Add the mushrooms and cook until they begin to wilt and give up their liquid, about 3 more minutes. Stir in the garlic and sauté for 1 more minute.
3 Brown the chicken: Stir in the chicken thighs and let them cook for about 3 minutes, stirring often, to brown the outside of the chicken. It’s fine if some pieces are still partially pink on the insides; the chicken will finish cooking in the pressure cooker.
4 Add the rice and the sauce: Use your spatula to pat the chicken and vegetables down into a fairly even layer. Sprinkle the rice over the top of the chicken in an even layer. Slowly pour the sauce over the rice, taking care not to disturb the layer. Use a spoon to nudge down any grains of rice that are clinging to the sides of the pot, so everything is covered with the cooking liquid.
5 Pressure cook the chicken and rice: Secure the lid on the pressure cooker. Make sure that the pressure regulator is set to the “Sealing” position. Cancel the “Sauté” program on the pressure cooker, then select the “Manual” or “Pressure Cook” setting. Set the cooking time to 15 minutes at high pressure. (For stovetop pressure cookers, cook for 12 minutes at high pressure.)
The pressure cooker will take about 10 minutes to come up to pressure before the cooking time begins.
6 Let the pressure release naturally for at least 10 minutes, then quick-release the pressure by immediately moving the vent from “Sealing” to “Venting.” Be careful of the steam! You can let the pot continue to depressurize naturally, which takes about 20 minutes total.
The sauce may look a little bit separated when you initially open the pot. Don’t worry, it’s fine! Just use a fork to gently fluff the rice and incorporate the creamy layer back into the casserole.
7 Serve the casserole: Spoon the casserole into shallow bowls or onto plates, digging all the way down to the bottom so you get both rice and chicken in each scoop. Sprinkle generously with chopped parsley and serve hot.
Leftovers will keep for about a week and can be warmed in the microwave.