1. Browning the chicken. Season both sides of the chicken breasts with salt and pepper. Heat the oil in a large (10 to 12-inch) skillet over medium-high heat. Using tongs, carefully lower the chicken breasts into the pan and cook them for about 1 minute on each side just until hey begin to brown slightly. Transfer the still-raw chicken to a plate.
2. Poaching in cream. Reduce the heat under the skillet to low. Add the shallot and cook, stirring constantly, until softened but not browned, less than 1 minute. Add the vermouth and cook for 30 seconds, then add the cream and half the tarragon. Return the chicken breasts to the pan and adjust the heat so that the cream gently simmers. Cover and cook until the chicken is firm and just cooked through, 4 to 6 minutes. To check for doneness, cut into the thickest part of a breast with a pairing knife ¿ there should be no sign of pink or translucence.
3. Finishing. Transfer the chicken breasts to a warmed serving platter or individual dinner plates. The sauce should be thick enough to lightly coat a spoon. If it is too thin, continue to simmer it for about 1 minute and it will thicken. Stir in the remaining tarragon and the lemon juice, then taste and season with additional salt and pepper if needed. Pour the sauce over the chicken and serve right away with buttered egg noodles.
Recipe courtesy of The Herbfarm Cookbook Published by Scribner, 2000.