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Wash shiitakes and barely cover with boiling water. Preheat oven to 200 C.
Cut carrots and onions into about 2 cm chunks. Saute in olive oil over medium-high heat until browned. Add garlic and saute a few minutes more. Add tomato puree and mix. Deglaze with red wine and cook for a minute. Add mushroom soaking liquid, stock base, thyme, bay leaves and allspice. Mix well. Add eggplant into 2 cm chunks. If necessary, add water until vegetables are barely covered.
Cover with a lid or aluminum foil and bake for 20 minutes. Remove cover and bake for 20 minutes more, or until sauce is thickened and carrots are done. Remove bay leaves and thyme stalks.
Serve with mashed potatoes.