Saute the onion, celery, and garlic in oil in a large skillet until the vegetables are tender. Add the ground beef, and cook until browned, stirring to crumble meat; drain well.
Add the mushrooms and next 5 ingredients; stir well. Reduce heat, and simmer, uncovered, 15 minutes.
Cook the spaghetti according to package directions; drain well. Place the spaghetti in a greased 13x9x2 inch baking dish. Top with sauce, and sprinkle with 1 cup cheese. Pour the milk over the cheese, and sprinkle with the remaining 1 cup cheese.
Bake, uncovered, at 350 degrees for 20 to 30 minutes or until cheese melts and the mixture is thoroughly heated.