Dice the chicken breasts into bite-sized cubes, then season them with salt and pepper.
Finely dice the onion. Wipe the mushrooms clean with a damp cloth and slice them thinly.
Heat the olive oil in a large, deep skillet over medium heat. Once hot, add the diced onion and a pinch of salt. Sauté for about 5 minutes, stirring occasionally, until softened.
If the onions start to stick or brown too quickly, add a splash of water (about 4 tablespoons) and continue to sauté for another minute.
Add the seasoned chicken to the skillet. Cook, stirring occasionally, until the chicken is white on all sides, about 5 minutes. It doesn't need to be fully cooked through at this stage.
Add the sliced mushrooms to the pan, season them with a little more salt and pepper, and stir to combine. Cook for about 5 minutes, allowing the mushrooms to release their water and begin to brown.
While the mushrooms cook, finely chop the fresh parsley.
Pour the half-and-half (or heavy cream) into the skillet and add the chopped parsley. Stir everything together.
Bring the sauce to a gentle simmer and let it cook for another 2-3 minutes, allowing it to thicken slightly. Taste and adjust the seasoning with more salt or pepper if needed.
Serve the creamy chicken and mushrooms immediately with your favorite side, such as mashed potatoes, gnocchi, rice, or pasta. Enjoy!