Welcome to intermediate-to-pro cooking. If you just want to refuel your carbohydrates, go here. On the other hand, if you're looking for a gustatory experience, stick with me. By the way, I have no intentions to offend the author of chicken in tarragon sauce, but here's how to do this properly:
Scald tomatoes, peel and scoop out seeds.
Chop and simmer with 2 tbsp olive oil, salt and sugar.
Cut chicken into 8 pieces, season and sauté in butter and 2 tbsp olive oil.
Add onion, shallots, garlic cloves (whole), tarragon stalks and bay leaves.
Steam for 20 minutes at 375°F/190°C, adding the tarragon vinegar in small amounts.
Skim grease, add olive oil, remove the chicken and keep it warm.
Add chicken broth and white wine. Mix Dijon mustard and tomato puree, add this too and reduce to half its volume.
Now add the tomatoes and cream, put the chicken back and cook for another 15 minutes.
Finally, add chopped tarragon.
Slice the mushrooms, quickly fry them in olive oil, salt and sprinkle with lemon juice. Add those as well.
You should probably make some basmati, too.
The secret to the utter deliciousness is that the tarragon vinegar evaporates and scents the chicken. Cook this for the woman of your dreams and there's a significant chance that she will be all over you1. I take no responsibility for any quality time that potentially ensues.
1Supposedly works for boys, too.