Heat your oven to 225 degrees. Generously dust the chicken breasts with salt and pepper. Then melt 1 tablespoon of butter in a skillet over medium-high heat. Add the chicken and cook for about 3 minutes per side, until browned. Then place on a baking sheet and bake the chicken while you prepare the sauce.

Using the same skillet, melt 1 tablespoon butter over medium heat, scraping up any browned bits from the chicken. Then add the mushrooms. Season with salt and pepper, and toss the mushrooms to evenly coat them. After 3 minutes, add ¼ cup of the white wine, and the sliced shallots. Saute until the shallots are soft, then remove the vegetables from the skillet and set aside.

Again using the same skillet, melt the remaining butter, and whisk in the flour. Then whisk in the milk. Bring the mixture to a slow and steady boil, whisking constantly for one minute, while the sauce thickens.

Once the milk mixture has thickened, whisk in the chicken broth, lemon juice, mustard, and garlic. Bring to a simmer and add the tarragon and thyme. Stir frequently, letting the mixture slowly simmer and reduce. Add salt and pepper to taste. Add the mushrooms and shallots to the sauce, and add the spinach, letting it wilt. Stir to combine.

After cooking in the oven for 20 minutes, the chicken should be ready. Serve the chicken with a generous amount of the sauce and vegetables poured over.