1. For the Chicken: Adjust oven rack to middle position and heat oven to 200°F. Season both sides of each cutlet with salt and pepper. Heat 2 teaspoons oil in 12-inch skillet over medium-high heat until smoking. Place 4 cutlets in skillet and cook without moving them until browned, about 2 minutes. Flip cutlets and continue to cook until second sides are opaque, 15 to 20 seconds. Transfer to large ovensafe plate. Add remaining 2 teaspoons oil to now-empty skillet and repeat to cook remaining cutlets. Cover plate loosely with foil and transfer to oven to keep warm while making pan sauce.

2. For the Sauce: Add oil to empty skillet used to cook chicken and return pan to medium heat. Add leek and cook, stirring often, until softened and browned around edges, 2 to 3 minutes. Add flour and cook, stirring constantly, 30 seconds. Add broth and vermouth, increase heat to medium-high, and bring to simmer, scraping pan bottom to loosen browned bits. Simmer rapidly until reduced to 3/4 cup, 3 to 5 minutes. Stir in any accumulated chicken juices; return to simmer and cook 30 seconds. Off heat, whisk in mustard, tarragon, and butter; season with salt and pepper. Spoon over cutlets and serve immediately.

Serves 4