Rinse and dry the chicken thighs and season with salt and pepper.
Heat 1 tablespoon olive oil in a Dutch oven over medium-high heat. Brown the thighs on both sides, working in batches if needed. Remove the chicken and set aside.
Add the remaining 1 tablespoon olive oil to the Dutch oven and cook the onions until soft, about 5 minutes. Add the mushrooms and continue to cook until the mushrooms have softened, 3 to 5 minutes. Stir in the garlic and cook until fragrant, about 2 minutes. Add the tomatoes and flour and cook, stirring, to remove the raw flour flavor, about 3 minutes. Stir in the tarragon. Turn up the heat and deglaze the pan with the white wine, allowing to bubble for a minute or two. Return the chicken to the Dutch oven. Add enough chicken stock to reach halfway up the sides of the chicken. Cover, place in the oven, and braise for 45 minutes, removing the lid halfway through.
When finished, remove the chicken from the Dutch oven and set aside. Add the mustard and sour cream and whisk to blend well. Return the chicken to the pan and allow the flavors to meld before serving, about 5 minutes. Serve over Super Buttered Noodles.
Super Buttered Noodles:
In a large pot filled with boiling water, dissolve the bouillon cubes and cook the noodles according to package directions. Drain the noodles in a colander and then nestle the colander into the pot so some of the pasta water goes into the pot as the pasta continues to drain. Remove the colander and stir the butter and sour cream into the pot until the butter melts. Add the parsley and the noodles. Season with salt and pepper. Toss to combine well. Pour into a serving bowl and serve.