No you don't, although I find the oven to be a great (and low maintenance) way to cook the stew slowly and build up lots of flavor. If you want to skip using the oven, then simply keep cooking the stew on the stove on a slow simmer, covered (maybe on low-medium heat) for about 20-30 minutes. Then, add the mushrooms and keep cooking for another 20-30 minutes keeping the cover off this time and stirring once in a while. The stew is done when the veggies are tender and the gravy thicker.