Pat the chicken breasts completely dry and season both sides generously with salt, pepper, and Italian seasoning.
Heat olive oil and butter in a large skillet over medium-high heat. Once sizzling, add the chicken breasts in a single layer. Cook for 4-6 minutes per side, until golden brown and cooked through. Remove chicken from the skillet and set aside on a plate.
Reduce heat to medium. Add the minced garlic to the skillet and sauté for 30-60 seconds until fragrant, being careful not to burn it.
If using, pour in the white wine to deglaze the pan. Scrape up any browned bits from the bottom with a wooden spoon. Let it simmer for 1-2 minutes until mostly evaporated.
Pour in the chicken broth, bring to a simmer, and let it reduce for 2-3 minutes. Stir in the heavy cream and grated Parmesan cheese. Continue stirring gently over a low simmer until the cheese is melted and the sauce has thickened.
Stir in the drained sun-dried tomatoes and let them simmer in the sauce for one minute.
Add the fresh spinach to the skillet. Stir it into the hot sauce until it wilts completely, which should take about 1-2 minutes.
Return the seared chicken and any accumulated juices from the plate back to the skillet. Nestle the chicken into the sauce and spoon some over the top. Let it simmer for another minute to heat through before serving.