Cut the chicken breasts lengthwise for 4 cutlets total. Place between sheets of wax paper/plastic wrap and pound slightly until larger & slightly thinner. Sprinkle breasts with salt, pepper & garlic powder, then dredge in flour.
In a large skillet, add olive oil and 1 Tbs butter over medium-high heat. When oil/butter is hot & bubbly, add the floured cutlets. Cook 4-5 minutes per side until golden. Transfer chicken to a plate & tent with foil.
Add wine to the pan and deglaze for 1-2 minutes.
Add tarragon and 2 Tbs butter and continue simmering for another 2-3 minutes.
Add cream and simmer 2-3 minutes.
Reduce heat to medium and return chicken breasts to the pan, Cook for 5 minutes or until chicken is cooked through and sauce has thickened to desired consistency.
Plate chicken and spoon sauce over top. Garnish with sprinkle of fresh parsley if desired.