Start by patting the chicken breasts dry with paper towels. Season both sides generously with salt and freshly ground black pepper. Dredge each breast in flour, shaking off any excess.
In a large skillet, heat the olive oil over medium-high heat. Once hot, add the chicken breasts to the skillet. Cook for about 6-7 minutes on each side, or until they are golden brown and cooked through. Remove the chicken from the skillet and set aside on a plate.
In the same skillet, add the minced garlic and sauté for about 30 seconds until fragrant. Pour in 1 cup of Swanson Chicken Broth and scrape up any browned bits from the bottom of the skillet.
In a small bowl, whisk together the remaining 1 tablespoon of chicken broth, dried basil, lemon juice, and cornstarch until smooth. Slowly stir this mixture into the skillet with the garlic and broth. Bring to a simmer and cook for a few minutes until the sauce begins to thicken.
Lower the heat and stir in the heavy cream and Pecorino Romano cheese. Allow the cheese to melt and blend into the sauce, creating a creamy texture. Adjust the seasoning with salt and pepper to taste.
Return the chicken breasts to the skillet, spooning the creamy sauce over the top. Let them simmer for an additional 2-3 minutes to soak in the flavors. Garnish with freshly chopped parsley before serving.