Roast the Turkey Wings:
Preheat oven to 400°F (200°C).
Place turkey wings, carrots, celery, and onion on a large roasting pan. Drizzle with olive oil, toss to coat, and roast for 1 hour, turning halfway, until golden brown.
Simmer the Stock:
Transfer roasted turkey and vegetables to a large pot. Add chicken broth, water, thyme, rosemary, and bay leaves.
Bring to a boil, then reduce to a simmer and cook uncovered for 1 1/2 hours.
Strain the Stock:
Remove turkey wings and set aside (meat can be used for soup or sandwiches). Strain stock through a fine-mesh sieve into a large bowl or pitcher, discarding solids.
Make the Roux:
In a large saucepan, melt butter over medium heat. Whisk in flour and cook for 2–3 minutes until golden and nutty.
Finish the Gravy:
Slowly whisk in the strained stock, a little at a time, until smooth.
Simmer for 10–15 minutes until thickened.
Season with salt and pepper to taste.
Cool and Store:
Let cool completely before transferring to airtight containers for storage.