Clean the chicken drumsticks and season generously with salt and pepper. Let them sit for 10 minutes to allow the flavors to penetrate.
Dice the carrots and celery into small cubes, finely chop the onion, and crush the garlic.
Heat the olive oil in a deep skillet over medium-high heat. Sear the chicken drumsticks on both sides until lightly golden brown. Remove them from the skillet and set aside.
In the same skillet, sauté the onion, carrots, and celery until softened. Add the garlic and sauté for another 1-2 minutes until fragrant.
Sprinkle the vegetables with flour, stir well to coat, and then gradually pour in 200 ml of water, stirring constantly, until you have a thick sauce.
Return the chicken drumsticks to the skillet and stir in the sour cream. Reduce the heat to low, cover, and simmer for 20-25 minutes, or until the chicken is cooked through and the sauce has thickened and the flavors have melded together.
Serve the braised chicken hot, garnished with fresh parsley, and accompanied by cooked rice or mashed potatoes.
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