Saute the shallots and mushroom in 1 T of butter in a nonstick skillet over medium heat for about 4 minutes.
Add 1 cup of wine and 3/4 C of chicken broth and cook for 5 minutes, stirring frequently.
Remove the mushroom from the sauce to a small bowl.
Increase heat to high, cooking the wine mixture until it reduces to about 1/2 C (about 5-6 minutes), then pour over the mushrooms.
Decrease heat to medium high, sprinkle pepper generously over the chicken pieces and cook in 1 T of butter, in the same skillet, covered, for about 5-6 minutes per side, or until the chicken is done.
Place on a platter and keep warm.
Add 1/2 C of wine and the rest of the broth to the skillet and deglaze, boiling for about 1 minute.
Combine the cornstarch and lemon juice and add to the pan along with the basil leaves, and the retained mushroom sauce and bring to a boil for another minute, stirring constantly.
Serve the chicken pieces with the sauce spooned over them.
This tastes great served with pasta and vegetables.