Pound thicker parts of chicken breasts out even, to about 1/2-inch thickness.
Heat olive oil in a 12-inch skillet over medium-high heat.
In a shallow dish whisk together flour with 1/2 tsp each salt and pepper. Dredge both sides of chicken breast in flour mixture then transfer to heated skillet.
Cook until center reaches 165 in center of each piece, about 6 minutes per side. Transfer chicken to plate tent with foil.
Add garlic to skillet set over medium heat, saute until just light golden brown (not browned and burnt), about 30 seconds. Pour in 1 cup chicken broth, lemon juice and basil.
Let broth mixture simmer and reduce by about half, about 2 minutes. Stir together 1 Tbsp chicken broth with cornstarch pour into broth mixture and cook stirring constantly until slightly thickened, about 30 seconds.
Pour in cream then reduce to low, add Romano cheese and cook just until melted.
Return chicken to sauce, spoon sauce over chicken. Serve warm garnished with parsley.