Step 1
Season duck legs all over with salt and black pepper.
Step 2
Heat vegetable oil in a large skillet over high heat. Place duck legs skin-side down in hot oil and cook until browned 2 to 5 minutes; turn and cook until browned on the other side 2 to 4 minutes more. Transfer legs to a plate; pour rendered duck fat into a bowl.
Step 3
Pour water into the skillet and bring to a boil while scraping the browned bits of food off of the bottom of the pan with a wooden spoon. Remove from heat.
Step 4
Heat about 2 tablespoons duck fat and olive oil in Dutch oven medium heat. Cook and stir onion in hot oil and fat until golden brown 7 to 10 minutes. Add turmeric cinnamon nutmeg; cook and stir until fragrant 1 minute.
Step 5
Pour chicken broth pomegranate molasses honey and reserved water mixture from the skillet into onions; bring to a simmer.
Step 6
Grind walnuts to a fine powder in a food processor.
Step 7
Cook and stir walnuts in a skillet over medium heat until fragrant 2 to 3 minutes. Stir walnuts into broth mixture; place duck legs in broth to cover in broth. Reduce heat and simmer until duck legs are tender 3 to 4 hours. Transfer duck to a serving dish.
Step 8
Bring broth mixture to a boil; cook until reduced and desired sauce consistency is reached. Season with salt. Ladle sauce over duck legs.