Cook the Chicken: Heat the olive oil in a large skillet over medium-high heat. Season the chicken breasts with salt and pepper. Add the chicken to the skillet and cook for 6-7 minutes per side until golden brown and cooked through. Remove the chicken from the skillet and set it aside on a plate.
- Sauté the Vegetables: In the same skillet, melt the butter. Add the chopped onion and cook for about 3 minutes until softened. Add the garlic and cook for another minute until fragrant.
- Add the sliced mushrooms to the skillet and cook for 5-6 minutes, until the mushrooms are softened and browned.
- Make the Sauce: Pour the chicken broth into the skillet, scraping up any brown bits from the bottom of the pan. Stir in the heavy cream and thyme, then bring the mixture to a simmer. Let it cook for 5 minutes, allowing the sauce to reduce slightly.
- Add the Peas and Chicken: Stir in the peas and return the cooked chicken to the skillet. Spoon some of the sauce over the chicken. Let everything simmer together for an additional 3-5 minutes, until the chicken is heated through and the sauce has thickened.
- Serve: Garnish with fresh parsley and serve immediately. This dish goes well with rice, mashed potatoes, or pasta.