Preheat oven to 425 degrees F.
Place the turkey carcass, bones and leftover meat, and vegetables into a large stockpot.
Drizzle everything with the olive oil and stir around to ensure everything is coated.
Place the pot in the oven and roast for 30 minutes, stirring things around halfway through cooking to roast all sides evenly.
Remove the pot from the oven and place on the stovetop, turning the heat to medium.
Pour in enough water to cover all the bones and vegetables.
Add in the herbs and peppercorns.
Bring to a boil over medium heat, cover and simmer, turning the heat to low for at least 4 hours.
Check and replace any water as needed to keep everything covered.
After 4 hours has passed, remove from heat and allow to cool.
Strain the broth through a fine sieve strainer, discarding all the vegetables and bones.
Pour broth into jars or other storage containers and store in the refrigerator.
Broth can be stored in the refrigerator for 3-5 days, or in the freezer for up to 3 months.