I made what is probably my best batch of bouillon ever today. I used a whole chicken carcass and your standard aromatics. I did not brown the chicken - rather, I removed the backbone and reserved it, removed the chicken's keel, and thus halved the carcass lengthwise, and rubbed the pieces with salt, pepper, and dried rosemary and thyme - this went into the boiling water along with the skin and all the edible offal (heart, liver, giblets), neck, and the reserved bones. I used the standard aromatics - onion, celery, and carrot.
The bouquet garni was really nothing too special, but the outcome was better by far than my previous attempts. Two sprigs of fresh parsley, two bay leaves, and the hard upper leaves of a leek. My bouquet garni's only real difference is my addition of a cinnamon stick. However, I'm sipping a cup of the bouillon as I read through coursework, and while the cinnamon is barely noticeable, the overall flavor profile of the bouillon is earthy, with a sweet-savory finish. The chicken flavor stands out as the foundation, while the herbs, pepper, and aromatics seem to really synergize. I did not add any wine to this bouillon, though I usually add a splash of a dry white. I just didn't have any on hand.
Some other broths I have made have included shiitake mushrooms, burdock, and other Asian ingredients such as star anise. I had the idea of adding cinnamon from some Asian broths and braises, which include cinnamon in the flavoring mix - typically these recipes are dominated by a sweet-salty taste mellowed and boosted by a generous amount of rice wine.