Slice the chicken breasts in half horizontally to create 4 thinner cutlets. Season both sides generously with salt and pepper.
In a large cast-iron skillet, heat the olive oil and butter over medium-high heat. Add the chicken cutlets and cook for 4-5 minutes per side until golden brown and cooked through (165°F internally). Remove the chicken to a plate and set aside.
Reduce the heat to medium. In the same skillet, add the minced garlic and chopped sun-dried tomatoes. Sauté for 1 minute until fragrant, scraping up any browned bits from the bottom of the pan.
Pour in the chicken broth, heavy cream, and Italian seasoning. Bring to a gentle simmer. Let it bubble and reduce for 3-4 minutes until it starts to thicken slightly.
Stir in the fresh baby spinach and let it wilt (about 1 minute). Remove from heat and immediately stir in the grated parmesan cheese until the sauce is smooth and creamy.
Return the chicken cutlets (and any resting juices) to the skillet, spooning the creamy sauce over the top. Serve immediately over pasta or with crusty bread.