Wash chicken thighs and pat dry with a paper towel. Then rub them with salt, pepper, and a generous amount of Creole or your favorite spice mix.
Heat a Dutch oven or skillet with a tablespoon of oil over medium-high heat (I used a 12-inch skillet). Add the chicken thighs skin-side up to the pan, browning for 4-5 minutes. Flip and brown on the other side. Remove the chicken to a plate and optionally wipe the pan clean with a paper towel.
Add another tablespoon of oil to the pan if needed. Sauté the onions, celery, garlic, bay leaf, thyme, and mushrooms until soft (2-3 minutes). Then add the flour and stir for about a minute.
Pour in the chicken stock and wine, stirring constantly, until the sauce thickens slightly (4-5 minutes).
Next, add the cream, adjust seasoning to taste with salt and pepper, and return the chicken to the pan.
Cover the pan and lower the heat to medium-low. Simmer until the sauce slightly thickens and the chicken is almost cooked through (12-15 minutes).
Take the lid off, and then stir in the carrots. Put the lid back on and simmer until the carrots and chicken are almost done.
Add the asparagus, put the lid back on, and cook until the chicken reaches an internal temperature of 175-180℉ (80-85℃) and the asparagus is tender (7-10 minutes).
Serve right away with rice or potatoes and a side salad.