How to Make It
Cover dried morels with 1 cup very hot water. Let stand until plump, about 15 to 20 minutes. Remove mushrooms, and set aside; strain soaking liquid to remove any grit. Set liquid aside. Leave small mushrooms whole; cut larger ones in half lengthwise.
Sprinkle chicken with 1 1/4 teaspoons salt and black pepper. Melt butter over medium in a large skillet. Add chicken, and cook until barely cooked on both sides, 1 to 2 minutes per side (do not brown). Transfer chicken to a plate.
Increase heat to medium-high. Add shallot to skillet; cook until softened, about 3 minutes. Sprinkle shallot with flour; whisk until smooth. Add wine; cook, stirring often, 2 minutes. Whisk in 1 cup reserved mushroom soaking liquid, and return chicken and morels to skillet. Reduce heat to medium-low; cover and cook until chicken is tender and cooked through, about 10 minutes.
Remove chicken from pan; whisk in cream, chopped tarragon, and remaining 1/2 teaspoon salt. Serve chicken on warmed plates; garnish with additional tarragon.