Step 1

Bring turkey carcass, scallions, ginger, star anise, cinnamon, fish sauce, sugar, coriander seeds, fennel seeds, and 4 qt. water to a boil in a large pot. Reduce heat, skim surface, and simmer until liquid is reduced by nearly half, 2–2½ hours.

Step 2

Strain broth through a fine-mesh sieve into a large saucepan; taste and adjust seasoning with salt if needed.

Step 3

Whisk mayonnaise and chili paste in a small bowl to combine. (If you like it extra-spicy, add more chili paste.)

Step 4

Heat leftover turkey in 1 cup broth in a medium skillet until warmed through.

Step 5

Assemble sandwiches with rolls, spicy mayonnaise, hoisin sauce, herbs, scallions, and bean sprouts. Serve with lime wedges and jalapeños alongside, as well as a small bowl of warm broth for dipping.