Season and Cook Chicken Thighs: Begin by generously seasoning both sides of the chicken thighs with Tony Chachere's original seasoning. Cook them over medium-high heat for a few minutes per side until nicely browned. Next, pour in the chicken broth, bring it to a boil, then lower the heat and let it simmer for about 20 minutes until the chicken is tender enough to shred. Once done, remove the chicken and broth from the pot.
Prepare Vegetables: In the same pot, add in the diced celery and carrots, seasoning them with Tony Chachere's spice and herb seasoning. Melt the butter, then add in the minced garlic.
Make the Base: Whisk in the flour and cook until it turns golden brown, which should take a couple of minutes. Afterward, return the chicken broth and shredded chicken to the pot, stirring well to combine. Pour in the milk and heavy cream. Reduce the heat to a simmer, cover the pot, and let it cook for about 5-10 minutes.
Prepare Dumplings: While the base is simmering, prepare the dumplings. Combine all the dry ingredients in a bowl, then gradually add the buttermilk, stirring until a dough forms. Shape the dough into dumplings about 1" in size.
Cook Dumplings: Gently place the dumplings into the pot, ensuring they are partially submerged in the liquid. Bring the mixture to a simmer, cover the pot, and let it cook for another 10-15 minutes, allowing the dumplings to cook through. Serve and enjoy your delicious chicken and dumplings!