Preheat oven to 350 degrees. Spray a 9x13 baking dish with cooking spray.
In a medium skillet heat oil over medium high heat. Add onion and cook until softened. Set aside to cool.
Bring a large pot of salted water to a boil. Using a small sharp knife, cut in a circle around the stem of the cabbage and remove the core. Place cabbage in the boiling water. After 2 minutes an outside leaf will come loose. Pull it off and out of the water with tongs. After another minute the next leaf will come loose. Remove and repeat this step until you have about 10 leaves.
Pat the leaves dry with paper towels. Cut the thick part of the rib from the bottom of each leaf, but don't cut more a third of the way into the leaf.
In a medium sized mixing bowl, combine the uncooked ground beef, mushrooms, cooked onion, rice and salt. With the stem side of the cabbage facing you, place 1/3 of the beef mixture in the center of each cabbage leaf. Fold bottom edge over the mixture and then fold the sides over and roll up into a tiny packet. Place cabbage rolls seam side down in the prepared baking dish.
In another bowl mix together tomato sauce, broth and paprika. Pour evenly over the cabbage rolls. Cover with foil and bake for 1 hour.