Heat olive oil in a large skillet over medium heat. Season the chicken breasts with Italian seasoning, salt, and pepper.
Add the chicken to the skillet and cook for 5 to 6 minutes per side, until golden and cooked through to 165°F. Transfer the chicken to a plate and cover loosely to keep warm.
Add the minced garlic to the same skillet and cook for about 30 seconds, just until fragrant.
Reduce heat to medium-low. Pour in the chicken broth and scrape up any browned bits from the bottom of the pan.
Stir in the softened cream cheese until mostly smooth, then stir in the sour cream.
Add the artichoke hearts and baby spinach. Stir until the spinach wilts and the sauce looks creamy.
Stir in the mozzarella and parmesan until melted and smooth.
Add the chicken back to the skillet and spoon the sauce over the top. Simmer for 1 to 2 minutes, just to warm everything through, then serve.