Trim the chicken, removing the tenders, and slice on an angle into 3/4-inch-thick pieces; season generously with salt and pepper.

In a 10-inch straight-sided saute pan, heat the oil over medium-high heat until it shimmers. Add half of the chicken and cook, flipping once, until lightly browned and just barely cooked through, 1 to 2 minutes per side. Transfer to a plate; repeat with the remaining chicken. Cover with foil to keep warm.

Return the pan to medium heat and, if it looks dry, add 1 tablespoon oil. Add the shallot and saute, stirring with a wooden spoon, until softened, about 1 minute. Pour in the vermouth and scrape the pan with the spoon to loosen any browned bits. Let the vermouth simmer until reduced slightly, about 2 minutes. Reduce the heat to low and add the cold butter 2 or 3 pieces at a time, stirring after each addition until completely melted. Stir in the tarragon, taste the sauce, and add salt and pepper as needed. Add the chicken and any accumulated juices to the sauce and turn to coat the chicken with the sauce. Serve immediately.

Drink Suggestions: A zingy-crisp white wine with herbal notes will match the tarragon in this dish. A Sauvignon Blanc from New Zealand would be delicious. -Tim Gaiser