Season the chicken pieces with salt and pepper then coat the chicken with the flour. Shake off excess.
Melt the butter in a large pot (like a dutch oven) over medium-high heat and brown the chicken pieces on all sides. Once browned, remove chicken from pot and set aside. (Chicken will not be cooked through yet, but don't worry, it's going back in the pot).
In the same pot, toss in the carrots, onions, and celery; cook for about 5 minutes. Toss in the fresh thyme and bay leaf.
Add the chicken broth to the pot, then add the browned chicken pieces. Cover the pot and let it simmer on medium heat for about 25 minutes (or until carrots are tender and chicken is cooked through).
While the chicken simmers, make the dumplings. Sift together the flour, cornmeal, and baking powder into a medium bowl. Slowly add the half and half in several batches, while gently stirring. Be gentle - over-mixing will result in tough dumplings.
Remove the chicken from the pot and shred the meat, discarding the bones. Add the chicken back into the pot, along with the half and half. Stir until combined. Fish out the bay leaves and remove them from pot.
Using a spoon, gently drop the dumplings into the pot (about tablespoon size). Cover the pot and let it simmer for about 15 minutes, or until the dumplings are fully cooked and tender. Let the chicken and dumplings sit for just a few minutes before serving. Enjoy!
Recipe by Shug & Spice at https://shugandspice.com/2017/09/18/homemade-chicken-and-dumplings/