1) Place the French ribs in a pot and cover with water. Add to the pot: 2 carrots, 1 chopped leak, 6 English peppercorns, 2 chopped red onions. Cook for about 4 hours until the meat is tender, remove meat from pot and do not pour out the liquid. Place meat in the refrigerator.
2) Peel the potatoes and boil until soft. Do not pour out the water. Remove the potatoes to a food processor and puree, add the cooking water, if necessary, until a velvety smooth texture is obtained. Remove the puree and pass through a dense sieve to remove any remaining lumps. Season the pureed potatoes with salt and ground black pepper only.
3) Sauce: Peel the red onions (3), chop and place in pot with a little olive oil and caramelize. Cut the mushrooms into quarters and add to onions until brown. Add 2 tablespoons of tomato paste and 1 tablespoon of brown sugar to the vegetables and mix until they stick to pot. Add 1 cup of red wine and mix so nothing sticks to bottom of pot. Take 3 cups of the broth from cooking the meat and bring to a boil. At this point add the thyme sprigs.
4) Once the meat has cooled, remove from the fridge and slice into 3 cm thick slices. Turn down the heat of the pot and use a spoon to make a depression in the sauce and arrange the meat in the shape of a rose. Pour a can of peas, cover the pot and cook for another 15 minutes.