2 5-ounce boneless, skinless chicken breasts, trimmed and tenders removed (see Tip)
1/2 teaspoon freshly ground pepper
1/4 teaspoon salt
1 tablespoon canola oil
1 medium shallot, minced
1 cup thinly sliced shiitake mushroom caps
2 tablespoons dry vermouth, or dry white wine
1/4 cup reduced-sodium chicken broth
2 tablespoons heavy cream
2 tablespoons minced fresh chives, or scallion greens
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. 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.