1. Mix the flour with the tarragon and season it with salt and pepper.
2. Pound gently the thicker part of the chicken breasts to even them, or butterfly them with a knife.
3. Dredge each chicken breast in the seasoned flour.
4. Heat the olive oil in a skillet and saute the chicken breasts until half cooked.
5. Remove the chicken breasts from the skillet and add the chopped shallots and sliced cremini mushrooms.
6. Saute for 3-4 minutes and deglaze with the Marsala wine.
7. Add the chicken broth and cream and return the chicken breasts to the skillet with the sauce.
8. Cook until the sauce is reduced and the chicken is fully cooked. Add more of the liquids if necessary.
9. Sprinkle the chicken breasts with the shredded Asiago cheese and broil under the broiler or in the oven for a few minutes, until the cheese is nicely melted.
10. Taste the sauce for salt and serve the Chicken Marsala with steamed vegetables and mashed potato.