Heat olive oil in a large deep skillet or Dutch oven over medium-high heat.
Season the chicken pieces with salt and black pepper.
Add the chicken to the skillet and cook for 5-6 minutes, stirring occasionally, until browned and cooked through. Remove chicken from the skillet and set aside.
In the same skillet, add the sliced mushrooms and cook for 4-5 minutes until they release their moisture and begin to brown.
Add the minced garlic to the mushrooms and cook for 1 minute until fragrant.
Pour in the chicken broth and bring to a simmer, scraping up any browned bits from the bottom of the skillet.
Reduce heat to medium-low and stir in the heavy cream, Parmesan cheese, dried thyme, and crushed red pepper flakes. Cook for 3-4 minutes until the sauce thickens slightly.
Add the fresh baby spinach to the sauce and cook for 2-3 minutes until wilted.
Return the cooked chicken to the skillet and stir to combine with the sauce and spinach. Cook for an additional 2 minutes to heat through.
Taste and adjust seasoning with additional salt and pepper if needed.
Serve hot, spooned over rice, pasta, or crusty bread if desired.