In a large skillet, saute onion in oil and butter for 2 minutes. Add garlic, cook 1 minute longer. Add mushrooms, cook 6-8 minutes longer or until they are tender and no liquid remains. Stir in salt and pepper.
In a large bowl, combine eggs, bread crumbs, cheese, parsley, thyme, and mushroom mixture. Crumble beef and sausage over mixture, mix well.
On a large piece of heavy duty foil, pat mixture into a 15X10 rectangle. Layer the proscuitto, cheese, basil, and tomatoes to within 1 inch of edge. Roll up jelly-roll style, starting with short side and peeling foil away while rolling. Seal seams and ends.
Place seam side down in a greased 13 X 9 baking dish. Bake uncovered at 350 degrees for 75-85 minutes or until no pink remains and a meat thermometer reads 160 degrees. Let stand for 5 minutes. Transfer meat to serving platter.