In a skillet, heat the olive oil over high heat. Dredge the breasts in flour and brown in the skillet. Place the chicken on a sheet pan and bake for 20 minutes at 350º or until done. Add the onion, the carrots, and the shallots to the skillet, saute until soft.
Add the stock and reduce by 50%. Add the mushrooms, cognac, and the wine. Add the tarragon and let simmer for about 8 minutes and then thicken with the roux.