In a large skillet over medium-high heat, melt the butter.
Add the onions and mushrooms, cooking until soft and golden.
In a large bowl, stir together cooked onions and mushrooms, cream of mushroom soup, chicken broth, balsamic vinegar, 1/2 c. Parmesan cheese, and 1/4 c. slivered almonds.
Fold in the green beans.
Spread into a lightly greased 2-qt. baking dish.
Bake at 350 degrees for 30 minutes, or until edges are bubbling.
Sprinkle with remaining Parmesan cheese and almonds.
Return to the oven for 4-5 minutes, or until cheese is melted, and the almonds are lightly browned.
Serve hot!