Toast chiles in a 5- to 6-qt. pan over medium heat, pressing down with a wide spatula and turning once, until fragrant, 1 to 2 minutes. Transfer to a plate.
Add oil, onion, carrot, and garlic to pan; cook, stirring occasionally, until onion is golden, about 10 minutes. Add chiles, broth, cinnamon, cayenne, almonds, and sesame seeds. Enclose turkey neck and giblets in a piece of cheesecloth and tie securely with string. Add to broth.
Heat mixture to boiling, then reduce heat and simmer, covered, for about 1 hour to blend flavors. Discard giblet packet.
Strain mole broth into a heatproof bowl. Purée contents of strainer in a blender with 2 cups of the broth until very smooth, 2 minutes. Add puréed mixture to bowl and set aside.
Strain turkey pan juices into a second heatproof bowl. Skim fat and pour 1/4 cup of it into a large saucepan; discard remaining fat. Measure 1 cup pan juices; save rest for another use.
Whisk flour into fat and cook over medium-high heat, whisking constantly, until it smells toasted, 2 minutes. Carefully whisk in the 1 cup pan juices and about 1 cup reserved mole broth. Add remaining broth and cook over medium-high heat, whisking often, until bubbling, about 12 minutes. Remove from heat and whisk in chocolate and vinegar. Pour into gravy boats.
Note: Nutritional analysis is per 1/3 cup gravy.