Save the turkey or chicken giblets, neck, and any pan drippings
Place giblets and neck in a saucepan with water, salt, and pepper
Simmer until fully cooked and tender
Remove giblets and neck from the broth
Chop the giblets finely and shred any meat from the neck
Melt butter in a skillet or saucepan
Whisk in flour to make a roux
Cook the roux until lightly browned
Slowly whisk in the giblet broth and pan drippings
Stir until smooth and thickened
Add chopped giblets and neck meat
Season with salt, pepper, and optional sage or thyme
Simmer briefly until heated through
Serve warm over biscuits, mashed potatoes, or turkey