Place chicken in a plastic bag or covered in saran wrap, using a tenderizer or a rolling pin, pound the chicken till it's flattened to about 1 inch. Add salt, pepper, and basil to season the chicken on both sides.
Add oil to a frying pan over med-hi heat. Let the oil get hot and add the chicken in searing about 5 minutes per side. Set aside and keep warm.
Lower heat to medium, add in the butter and the onion 3 - 4 minutes until soft. Add in the garlic and tomatoes and continue to saute for an additional minute.
Using 1/4 cup chicken broth, deglaze the frying pan by scraping, and then add in the remaining broth. Simmer uncovered 5 minutes to reduce the liquid by about half. Now add in heavy cream and stir for 30 seconds. Slowly add in cheese whisking to achieve a smooth consistency. Add in basil.
Place the chicken into the pan and cook an additional 6 - 8 minutes until chicken is completely heated through to 165℉.