Make sure salmon is completely dry by patting both sides. Season both sides of salmon with salt and pepper and Italian seasoning. Add ¼ cup of flour to bowl; coat salmon in flour coating evenly. Shake off excess flour.
Heat 1 teaspoon butter and 1 teaspoon olive oil in a large nonstick pan or skillet over medium heat. Swirl to combine butter and olive oil. Add the flour-coated salmon; sauté 4 minutes on each side. Transfer cooked salmon to plate and set aside.
Add 1 tablespoon butter to a pan and melt. Add the garlic; sauté until fragrant. Add wine and bring to a boil cooking until liquid almost evaporates, stirring occasionally. Add ¾ cup chicken broth with lemon juice; bring to a boil and cook for a further minute.
Mix 1 teaspoon cornstarch with 2 tablespoons reserved chicken broth, whisking well to combine. Add cornstarch mixture to the pan and stir to create a sauce. Cook until sauce slightly thickens, about 1 minute. If the sauce is not thick enough add remaining cornstarch and chicken broth, whisking well to combine and then add to the pan. Stir in ½ cup heavy cream, remove from heat and add the capers.
Place the salmon fillets in the pan, spooning sauce on top of the salmon. Sprinkle with chopped parsley, lemon slices, and pepper. Serve salmon over rice or pasta. Enjoy!