Preheat the oven to 180°C. Remove the giblets and rinse the duck well under cold water. Pat dry with paper towels. Rinse and drain the giblets. Prick the duck skin all over.
Heat the oil and half the butter in a large, flameproof casserole or deep roasting pan. Add the duck, breast side down, and fry for 3–4 minutes, or until the breast is well browned. Turn and brown the underside. Remove the duck, add the giblets and fry them for 2–3 minutes, or until lightly browned. Remove and set aside. Pour off all the fat from the casserole or pan and wipe clean.
Return the duck and giblets to the casserole or roasting pan, add the stock and bring to the boil. Remove from the heat, cover and place on a rack near the top of the oven for 30 minutes.
Take the casserole or pan out of the oven, remove the giblets and add the peas, herbs and seasonings. Cover and return to the oven for 1 hour, or until the duck is cooked.
Remove the duck from the casserole or pan and place on a heated serving dish. Lift out the peas with a slotted spoon and put them around the duck. Cover and keep warm.
Soften the remaining butter and mix in the flour. Gradually add the mixture to the duck stock and, with a wire whisk, stir on low heat until slightly thickened. Strain into a heated sauceboat. Garnish the duck with the mint or marjoram sprigs and serve with the sauce and sliced, minted new potatoes, if desired.