Place first 6 ingredients in a saucepan; bring to a boil. Cook 6 minutes or until reduced to 1 1/4 cups. Remove solids with a slotted spoon; discard.
Cut chicken breast halves in half horizontally to form 8 cutlets. Sprinkle evenly with 1/4 teaspoon salt and 1/4 teaspoon pepper. Place flour in a shallow dish; dredge chicken in flour. Heat a large skillet over medium-high heat. Add 1 tablespoon oil and 1 teaspoon butter to pan; swirl until butter melts. Add 4 cutlets to pan; cook 2 minutes on each side or until golden. Remove from pan; keep warm. Repeat procedure with remaining 1 tablespoon oil, 1 teaspoon butter, and 4 cutlets.
Return skillet to medium-high heat. Add mushrooms and onions; cook 5 minutes or until browned, stirring occasionally. Add stock mixture; bring to a boil, scraping pan to loosen browned bits. Combine 1 tablespoon water and cornstarch in a small bowl. Stir cornstarch mixture into stock mixture; cook 1 minute or until sauce thickens. Stir in remaining 1/4 teaspoon salt, remaining 1/4 teaspoon pepper, and tarragon. Spoon sauce over chicken.
I made a few substitutions when I tried this recipe, but it came out great.
1) Boneless pork cutlets instead of chicken.
2) Pre-packaged finely chopped mirepoix (Wegmans' brand) instead of the carrot/celery stalk/onion. What can I say, I'm a lazy cook!
3) Freeze dried tarragon instead of fresh.
4) I left the mirepoix and garlic in the sauce base instead of straining it out, and skipped the cornstarch step (I added the tarragon in at this step). The finely cut vegetables gave the sauce enough heft for me, and the extra vegetables bulked up the meal enough that I didn't need to add more than a side salad.
Great quick dish. I used 1 large shallot (1/2 in the sauce, 1/2 diced when you add the mushrooms), sliced mushrooms, and 1/2 package of dried assorted mushrooms in the sauce prep (tons of extra flavor to the chicken stock) removed along with the other veggies. This will be one of my go-to meals for a nice evening.
The tarragon definately makes this chicken dish special. As another reviewer did, I also opted not to use pearl onion (don't like them), instead I used coursely chopped yelIow onion. I made the suggested sides; Quinoa w/ Toasted Pine Nuts and Snap Pea and Radish Saute; delicious.