Combine flour, salt and pepper in a Ziploc bag. Add chicken; shake to coat.
Heat 2 tablespoons of olive oil in a non-stick skillet over medium-high heat. Add coated chicken. Cook until golden brown, 3 to 4 minutes per side. Remove from skillet. Wipe out skillet with paper towel.
Heat 2 tablespoons of butter in the same skillet over medium high heat. Add the peppers and onions. Cook for 2 to 3 minutes, or until vegetables just start to become tender. Remove from pan.
Melt remaining 2 tablespoons of butter in skillet. Whisk in flour, garlic, oregano and basil. Cook for 30 seconds or until garlic is fragrant. Add wine and chicken broth. Whisk until thickened and bubbly. Reduce heat to medium; cook, stirring occasionally until reduced by a half, about 20 minutes.
Add cream, Parmesan cheese and lemon juice. Stir until cheese has melted and the sauce is well combined. (See Tip 5)
Return the peppers and onions along with the chicken to the sauce. Stir to coat and heat for several minutes until chicken is heated through. Correct the seasonings.
Spoon chicken and sauce over angel hair pasta. Sprinkle on additional grated Parmesan cheese and top with sliced green onion.
Yield: 4 to 6 servings. (See Tip 6)