Heat the oil in a heavy-bottomed frying pan and cook the duck, skin side down first, over medium heat until brown all over. Remove and set aside, reserving 4 tbsp of the cooking fat.
Return 2 tbsp of the fat to the pan. Add the onion, carrot and thyme and cook over medium heat for 5 minutes or until onions are soft.
Add the stock and tomato and bring to a boil. Reduce heat and simmer 30 minutes, with the lid slightly askew, until the sauce has thickened and reduced.
Cool slightly, then puree in a food processor until smooth. Return to the pan with the duck and simmer gently over low heat for 30-40 minutes or until the duck is tender.
While the duck is cooking, peel the pears, halve them and core them, leaving the stem intact. Place the pears in a saucepan with the cinnamon and just cover with cold water. Bring to a boil, reduce heat and simmer gently for 5 minutes our until the pears are tender but still firm to the bite. Remove the pears, cover to keep warm and add 1/2 cup of the pear poaching liquid to the tomato sauce.
Remove the duck from the sauce and keep warm.
Grind the almonds, garlic and brandy in a mortar and pestle or small blender to make a smooth paste. Add to the tomato sauce, season to taste and cook for another 10 minutes.
Arrange the duck pieces on a serving platter and pour the sauce over the top. Arrange the warm pears around the duck and serve.