Take note of the small size of the breast and keep in mind, the sauce is just enough to coat 2 small breasts. Double the sauce should you desire more. Considering all, it's pretty healthy. No small wonder it comes from Eating Well.
Season chicken with pepper and salt on both sides.
Heat oil in a medium skillet over medium heat. Add the chicken and cook, turning once or twice and adjusting the heat to prevent burning, until brown and an instant-read thermometer inserted into the thickest part registers 165°F, 12 to 16 minutes. Transfer to a plate and tent with foil to keep warm.
Add shallot to the pan and cook, stirring, until fragrant, about 30 seconds. (I like to let them carmelize.) Add mushrooms; cook, stirring occasionally, until tender, about 2 minutes. Pour in vermouth (or wine); simmer until almost evaporated, scraping up any browned bits, about 1 minute. Pour in broth and cook until reduced by half, 1 to 2 minutes. Stir in cream and chives (or scallions); return to a simmer. Return the chicken to the pan, turn to coat with sauce and cook until heated through, about 1 minute.