First start the broccoli in a large pot with little water and cook until done. Also start the rice. The bagged rice should only take 10 minutes.
Saute the onions and celery in butter in a large skillet. Cook until clear. Once done, add the Cheez Whiz and let it cook down (med - med/high heat). Add the mushroom soup and the chicken soup. Again let it cook down. Now, add the broccoli.
Line the bottom of a lasagna dish with both bags of rice. Then add the broccoli mix to the pan. Add the French's onions to the top.
Place in a 350 degrees F preheated oven and cook for 20-25 minutes, just until the onion topper is a little darker brown.