1. Place potatoes in a large pot. Fill pot with cold water to cover the potatoes. Bring potatoes to a simmer and cook until tender, about 30 minutes (they should be easily pierced with a fork).
2. In another saucepan, sauté onion in 1 tablespoon olive oil for about 5 minutes. Add cranberries, thyme, vinegar, and 1⁄4 cup water. Let simmer for about 10 to 15 minutes, until everything has married together. Remove cranberry onion jam from the pan and set aside in a bowl. Wipe pan and place back on the heat.
STOP! AS CRANBERRY JAM SIMMERS, CLEAN POTATO POT AND FIRST SAUCEPAN.
3. As the potatoes cook, in a saucepan, heat 2 tablespoons olive oil over medium- high heat. Add leeks and cook until softened, 5 to 7 minutes. Add the milk and bring to a simmer. Season with salt and pepper. Turn off heat and set aside.
4. When potatoes are tender, drain them and add hot milk leek mixture. Mash well with a potato masher and mix until smooth. Season to taste, cover with foil, set aside.
5. Add 1 tablespoon olive oil to the pan. Cook sausages over medium-high heat until well browned and firm to the touch, about 5 to 7 minutes, turning all the time. Work in batches, if necessary, to avoid overcrowding.
6. Scoop a mound of mashed potato onto the center of a plate, stick two sausages in the mash, and top with cranberry onion jam to serve.
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