Heat 2 tbsp of the oil in a skillet over medium heat; cook onion, mushrooms and garlic until softened, about 5 minutes.
Add bulgur and sun-dried tomatoes and stir until coated.
Add stock and bring to a boil then reduce heat and let simmer covered for 20 minutes or until the liquid is absorbed. Transfer to bowl and set aside.
Preheat skillet to medium heat and add oil.
Peel 2 inch wide strips of skin from opposite sides of eggplants and discard.
Cut each eggplant lengthwise into 6 slices about 1/4 inch thick. Brush both sides with oil and sprinkle with salt and pepper. Grill slices in oiled skillet turning once until golden and tender about 10 minutes. Transfer to tray and set aside.
Preheat oven to 375 degrees.
Stir goat cheese into bulgur mixture.
Lay slice of eggplant on work surface and spread with 1/4 cup bulgur mixture starting at narrow end, roll up. Place seam side down on cooking tray and then repeat with remaining eggplant.
Pour tomato sauce into a 13 x 9 inch baking dish. Place eggplant rolls on top seam side down. Cover dish with aluminum foil and bake for 20 minutes or until sauce is bubbling.