Season the chicken breasts with salt and pepper on both sides.
Heat olive oil in a skillet over medium heat. Add the chicken and cook until golden brown on both sides (about 5-7 minutes per side). Remove from the skillet and set aside.
In the same skillet, melt butter and sauté garlic until fragrant, about 30 seconds.
Add the mushrooms and cook for about 5 minutes, until tender.
Pour in the chicken broth and scrape up any browned bits from the bottom of the skillet.
Stir in the heavy cream, then add spinach and cook until wilted.
Return the chicken to the skillet and simmer until the chicken is cooked through, about 5-7 minutes.
Serve immediately, garnished with fresh herbs if desired.
Notes
If you prefer a thicker sauce, simmer it longer to reduce.
You can make the sauce lighter by using half-and-half instead of cream.