Season both sides of the chicken breasts with salt and pepper.
Heat olive oil in a large skillet over medium heat. Add chicken and cook until golden and cooked through, about 6–8 minutes per side. Remove and set aside.
In the same skillet, melt butter and sauté garlic until fragrant, about 30 seconds.
Pour in chicken broth, scraping up any browned bits from the pan.
Stir in cream and Parmesan. Let simmer for 3–4 minutes until slightly thickened.
Add spinach and Italian seasoning. Cook until spinach wilts, about 2 minutes.
Return chicken to the pan, spoon sauce over top, and let it simmer for another 2 minutes before serving.