Pat chicken breasts dry with paper towels and season generously with salt and pepper on both sides. Heat olive oil in a large 12-inch skillet over medium-high heat until shimmering, then carefully add chicken and cook 5-6 minutes per side until golden brown and internal temperature reaches 165°F.
Remove cooked chicken to a cutting board and let rest for 3 minutes before slicing into bite-sized pieces. In the same skillet, melt butter over medium heat and add diced onion, cooking until softened and fragrant, about 3-4 minutes.
Add minced garlic and sliced mushrooms to the skillet, stirring constantly and cooking for 2 minutes until mushrooms begin releasing their moisture. Pour in chicken broth, scraping up any browned bits stuck to the bottom of the pan using a wooden spoon.
Stir in heavy cream, parmesan cheese, dried thyme, and red pepper flakes, combining thoroughly and simmering for 3-4 minutes until the sauce thickens slightly. Return sliced chicken to the skillet and stir gently to coat with the creamy sauce.
Add fresh spinach by the handful, stirring gently as each addition wilts down into the cozy chicken spinach skillet recipe. Once all spinach is incorporated and wilted, which takes about 2-3 minutes, taste and adjust seasonings with additional salt and pepper as needed.
Squeeze fresh lemon juice over the entire skillet and stir one final time to combine flavors. Serve immediately while the dish is hot and the sauce is silky smooth and coating every ingredient.