Preheat oven to 425. Bring to a medium pot with two cups of water to a boil. Prepare a baking sheet with foil. Thoroughly rinse produce and pat dry. Peel and mince shallot. Quarter button mushrooms. Peel and slice carrot on bias. Stem and roughly chop parsley. Rinse and pat dry chicken drumsticks.
Cook the Chicken
Season the chicken drumsticks with half the creole seasoning. Heat 2 tsp. of olive oil in a medium pan over medium-high heat. Place chicken drumsticks in pan and cook for about 2 minutes per side then transfer to prepared baking sheet. Keep oil in pan and place chicken in oven and cook for about 12 minutes. Keep warm for plating.
Cook the Grits
Once water is boiling, whisk in grits and cook for one minute. Lower to a simmer, cover and cook for 5 -7 minutes. Season with ¼ tsp. of salt and pepper. Keep warm for plating.
Start the Sauce Piquant
Heat the same pan used to sear the chicken over medium heat. Add the shallot, carrot, mushrooms, and okra and cook for about 1 minute.
Finish the Sauce Piquant
Add the white wine and cook for an additional minute. Add creole seasoning, chicken base, tomato paste, and 1½ cups of water then bring to a boil. Reduce to simmer and cook for about 5 minutes.
Plate the Dish
Ladle a serving of grits in a bowl, then place drumsticks on top. Ladle some of the sauce piquant over the chicken, and garnish with chopped parsley.