Step 1

Heat the oven to 400°F with a rack in the lower-middle position. In a large Dutch oven over medium, melt 1 tablespoon of the butter. When the foaming subsides, add the onion and garlic and cook until lightly browned, about 5 minutes. Pour in the wine and bring to a simmer. Lay the thyme sprigs on the onion mixture.

Step 2

Using paper towels, pat the chicken dry then season with salt and pepper. Set the chicken breast side down over the thyme and onions. Cover and bake until the thickest part of the breast reaches 160°F and the thighs reach 175°F to 180°F, 55 to 65 minutes. Using tongs inserted into the cavity of the chicken, carefully transfer it to a large baking dish, turning it breast side up. Let rest for at least 15 minutes.

Step 3

Meanwhile, remove and discard the thyme sprigs. Tilt the pot to pool the liquid to one side and use a wide spoon to skim and discard the fat. Bring to a simmer over medium and cook until thickened and reduced to about 1 cup (with solids), about 5 minutes. Off heat, whisk in the remaining 4 tablespoons butter, the lemon juice and mustard. Taste and season with salt and pepper.

Step 4

Remove the legs from the chicken by cutting through the hip joints. Remove and discard the skin from the legs, then separate the thighs from the drumsticks. Remove the breast meat from the bone, remove and discard the skin, then cut each crosswise into thin slices. Arrange the chicken on a platter. Transfer the sauce to a bowl, stir in the tarragon and serve with the chicken.