Sauce: In a heavy saucepan cook the butter and the flour over moderately-low heat, whisking for 3 minutes, whisk in the stock and bring the mixture to a boil. Add the mushrooms, garlic and the bouquet garni and simmer the mixture for 25 minutes, skimming the froth, for 25 minutes. Strain the mixture through a sieve into another heavy saucepan, stir in the ham, sage and heavy cream; simmer the sauce until it is reduced to 3 cups. Add the pepper and salt to taste and keep the sauce warm, covered.
In a large skillet heat 2 tbs of the oil and 1 tbs butter over moderately-high heat until the foam subsides. While the fat is heating, pat the chicken breasts dry, season the chicken with salt and pepper. Brown the chicken on both sides, reduce heat and finish cooking. Serve the chicken with sauce.