In the same pan, over medium-high heat, saute the shallots until translucent. Add the mushrooms and cook until they give up their juices. Add the wine and let cook for about 5 minutes. Then reduce heat to medium-low, return the chops to the pan, cover, and let cook until the chops are tender, about 35 minutes. Transfer the chops to a platter and increase the heat under the pan of mushrooms and sauce and allow to reduce by two-thirds.
While the chops are cooking and the sauce is reducing, prepare the bulgur porridge which was traditionally served with venison as a digestive aid. Because it is pre-steamed, it can be soaked in boiling water to make it meal-ready. Put bulgur and salt in a mixing bowl. Add 2 1/2 cups boiling water, cover and let stand for 30 minutes.