1. Peel and thinly slice shallots. Slice mushrooms. Chop tarragon. Peel garlic. Juice lemon.
2. In a large skillet, heat ⅔ of the oil over medium heat. Add shallots and mushrooms and cook until tender and lightly browned. With slotted spoon, transfer to a small bowl.
3. On a plate, mix salt, tarragon, and flour. Use to coat chicken breast. In the same skillet, add the remaining oil and increase to medium-high heat.
4. Add chicken and cook, turning once, until golden brown.
5. Reduce heat to medium-low, cover and cook about 10 minutes longer, until internal temperature reaches 160F or juices run clear when pierced with a knife.
6. Place chicken on prepared plates and keep warm.
7. In a cup, mix cornstarch with broth. Pour into skillet and heat to boiling over high heat, stirring to deglaze the skillet.
8. Add garlic, lemon juice, and browned shallots and mushrooms. Pour over chicken and serve.