Slice the chicken breasts lengthwise to get 4 pieces. Lightly beat with a kitchen mallet if needed to even out the pieces. Season the chicken with some salt, pepper and flour.
Bring a large nonstick skillet to medium heat and add 1 tbsps. of olive oil. Sear the chicken on each side for 5 minutes until golden brown in color. Transfer the chicken to a plate and set aside. Cover with foil wrap.
In the same skillet, melt 1 tbsp. of butter and add in the flour. Mix to blend well. Once you have a smooth creamy texture, add in the heavy cream, chicken broth, salt, basil, spices and mix well. Let the sauce simmer for 2-3 minutes until it thickens up a little.
Add in the grated parmesan cheese and pesto sauce. Mix well and let the sauce simmer for about 1-2 minutes. Taste to make sure your salt and spices are to your liking.
Return the chicken back to the pan. Drench with some of the sauce and cover to simmer on low heat for 3-5 more minutes.
Remove from heat, garnish with some basil leaves and parmesan cheese (optional) and serve.