
Preheat oven to 400 degrees F.
Season chicken thighs with salt and pepper, to taste.
Melt butter in a large oven-proof skillet over medium high heat. Add chicken, skin-side down, and sear both sides until golden brown, about 2-3 minutes per side.
Place into oven and roast until completely cooked through, reaching an internal temperature of 175 degrees F, about 25-30 minutes. Set chicken aside and keep warm.
In a medium bowl, whisk together chicken broth, heavy cream, and flour; set aside.
Add garlic and shallot to the skillet, and cook, stirring frequently, until fragrant, about 2 minutes. Stir in carrots and mushrooms until just tender, about 4-5 minutes.
Stir in wine and stock mixture, scraping any browned bits from the bottom of the skillet; bring to a simmer.
Stir in asparagus until crisp tender, about 3-4 minutes. Stir in dill and tarragon until fragrant, about 1 minute; season with salt and pepper, to taste. Return chicken to the skillet.
Serve immediately.