In a medium skillet, heat oil over medium-high heat. Add onion and sauté until golden, 3 to 5 minutes. Stir in cinnamon and allspice, and cook until fragrant, about 1 minute. Add walnuts, pomegranate molasses, 1 3/4 cups pomegranate seeds, and veal and chicken stocks. Bring to a boil, reduce to a simmer, and cook until reduced and thickened, about 15 minutes. Remove from heat, set aside.
Score duck in a crosshatch pattern. Season with salt and pepper. Heat a large cast-iron skillet over medium heat. Add duck breasts, skin-side down, and cook until most of the fat has rendered and the breasts are almost cooked through, 15 to 20 minutes. Turn breasts over, and cook until medium-rare, 2 to 3 minutes. Remove from skillet; set aside. Let rest 10 minutes before slicing.
Transfer duck breasts to a work surface, skin-side down. Thinly slice on the bias. Transfer to plates, and top with sauce. Garnish with mint and the remaining 1/4 cup pomegranate seeds. Serve with potatoes and salad, if desired.