Step 1

Cut or break apart the turkey carcass so the bones can be browned in a pot. In a large Dutch oven over medium-high, heat the oil until shimmering. Add the turkey bones and cook, turning and stirring, until well browned, about 3 minutes. Add half the leeks and 1 teaspoon salt; cook, stirring, until the leeks are wilted and lightly browned, about 2 minutes. Add 3 quarts water, the garlic and bay. Bring to a boil over high, then reduce to medium-low and simmer, partially covered, until reduced by about one-third, 1 to 1¼ hours.

Step 2

Meanwhile, in a medium bowl, stir together the flour and ½ teaspoon salt. Make a well in the center of the flour and to it add ⅓ cup water. Using a silicone spatula or wooden spoon, begin incorporating the flour by stirring at the center and gradually drawing in more flour until a shaggy dough forms. With the heel of your palm, knead the dough in the bowl, swiping along the sides to incorporate dry bits. Lightly flour the counter and turn the dough out onto it. Lightly flour your hands and knead until smooth, about 4 minutes. Form the dough into a ball, wrap in plastic wrap and let rest at room temperature.

Step 3

When the broth is ready, strain it through a fine-mesh strainer into a large (at least 4-quart) saucepan; discard the solids. Measure ½ cup broth into a small bowl or liquid measuring cup, then whisk in the mustard; set aside. To the broth in the saucepan, add the remaining leeks, the carrots, celery, gravy (if using) and ½ teaspoon pepper. Bring to a simmer over medium, then cook, uncovered and stirring occasionally, until the vegetables are tender, about 10 minutes.

Step 4

Unwrap the dough. Working beside the pot, hold the dough in one hand. With your other hand, pull and stretch 1-inch bits of the dough, flattening them between your thumb and forefinger, then tear them off and drop into the broth. Continue until you have used all the dough. Stir in the turkey meat. Bring to a simmer over medium-high and cook, stirring, until the noodles are tender, about 5 minutes.

Step 5

Stir in the mustard mixture. Off heat, taste and season with salt and pepper. Serve sprinkled with parsley or dill.