Heat 1 tbsp olive oil in a large stockpot over medium heat, add rough chopped carrots, celery, onions and garlic into the large stockpot. Sauté for approximately 2 minutes until fragrant. Add the turkey carcass, and pour enough cold water into the pot to cover entire carcass (any more will make the broth weak). Add the bay leaves, whole fresh herbs, and peppercorns.
Allow the water to slowly come to a boil. Lower heat to medium-low, and gently simmer partially covered for 1 ½ - 2 hours, or until turkey meat falls off the bones. As stock cooks, skim and discard impurities that rise to the surface. Add more water is needed to keep the carcass fully submerged while simmering. You can break up the turkey carcass as it cooks to reduce its size inside the stockpot.
Strain the stock through a fine sieve into a large bowl or pot. Use the stock immediately, or refrigerate to make soup the following day. If storing, cover turkey stock and allow it to cool in an ice water bath. Stir occasionally until it has finished cooling. Place the turkey stock in a storage container and refrigerate, or freeze.
Place “discarded” turkey on a cutting board until it is cool enough to handle, then sort through the meat piece by piece. Discard cooking vegetables, herbs, skin, bones and cartilage. Hand shred the good turkey meat into bite sized pieces, and place in a separate bowl. If making soup the following day, refrigerate overnight.