Season the exterior of the whole chicken with salt and black pepper, as well as red pepper flakes, if using.
Place the Dutch oven on your stovetop and set the burner to medium heat. Add cooking fat. Once the fat is sizzling, add the whole chicken, breast side down.
Allow the chicken breast to turn golden brown. This process will take 3-5 minutes.
Using a large wooden spoon or spatula, carefully flip the whole chicken so that it is now breast side up.
Allow the back of the chicken to turn golden brown. This process will take 3-5 minutes.
After chicken skin has browned on both sides, add white wine or white vermouth, if using, to the Dutch oven.
Next, add water to the Dutch oven to come halfway up the sides of the Dutch oven. Be careful not to completely submerge the chicken. The breast should still be visible. (See video.)
Turn the heat to high, and bring the mixture up to a boil. Cover the Dutch oven with a lid and turn the heat to low.
Allow the chicken and vegetables to simmer on low heat for 1 1/2 hours.
After the simmer time has elapsed, turn off the heat and transfer the chicken, vegetables, and broth to a large serving bowl. The chicken will be falling-off-the-bone tender.
Bring the serving bowl to the table and serve the chicken by shredding it from the bone and placing the shredded chicken into individual bowls along with some vegetables and broth.