Heat 1 tbsp olive oil in a large skillet over medium heat. Season the chicken with salt, black pepper, and Italian seasoning, then add to the pan and sear for 4–5 minutes per side until golden and cooked through. Remove the chicken and set aside. Reduce the heat to medium-low and add the remaining 1/2 tbsp olive oil. Add the diced shallot and cook for 2–3 minutes until softened, then stir in grated garlic and cook for about 30 seconds until fragrant.
Pour in a splash of white wine and scrape the bottom of the pan to release any browned bits. Add the chicken broth. Let it simmer for 2–3 minutes to slightly reduce and concentrate the flavor.
Lower the heat and stir in the heavy cream. Add the Boursin cheese and stir until fully melted and smooth, then stir in the parmesan cheese if using. Add spinach and stir just until wilted. Scrape the sauce to one side of the pan. Return the chicken to the skillet and spoon the sauce over the top. Let everything simmer together for 2–3 minutes until warmed through and slightly thickened. Garnish with fresh parsley or green onion and serve immediately.
