*Preheat the oven to 350 degrees. Coat two 1 ½ -quart casserole dishes with cooking-oil spray.
*Heat oil in a 12-inch skillet on medium. Dice chicken breasts into ½-inch pieces, and add to the skillet. When all the chicken is added, raise heat to medium-high.
*Peel and chop onion, adding it to the skillet as you dice. Stir and cook chicken and onion until the chicken is just cooked on the outside, 4 to 5 minutes. (The chicken will cook through in the oven.) Set aside.
*Place chopped broccoli and broccoli cuts in a colander, and rinse with warm tap water until the frozen block breaks apart. Set aside to drain.
*In a 3-quart or larger bowl, lightly beat the eggs. Add mushroom soup, cheddar and Swiss cheeses and mayonnaise. Stir well. Press broccoli with the back of a spoon to remove as much water as possible. Add it to the bowl. Add chicken and onions, and stir well.
*Pour the broccoli and chicken mixture, evenly divided, into prepared dishes. Smooth with the back of a spoon to even out mixture. Bake in the middle of the oven, uncovered, until the top begins to brown and the edges bubble, about 25 minutes.
*Remove from the oven, and sprinkle half the crumbs evenly on top of each casserole. Continue to bake, uncovered, until the crumbs brown, about 10 more minutes.
*After they are baked, the casseroles may be refrigerated for 3 days or frozen for up to a month. If frozen, allow the casserole to thaw for 24 hours in the refrigerator. Set the refrigerated casserole out while you preheat the oven to 350 degrees. Warm for 20 to 30 minutes covered with aluminum foil until heated through. Uncover for the last 5 to 10 minutes to crisp the crumbs.
Notes: This recipe uses 2 types of broccoli. The broccoli cuts (smaller pieces than florets but not quite as fine as chopped) add texture, while chopped broccoli is a necessary binder. If you can't find frozen cuts, substitute florets or spears, and chop into bite-size chunks. If you can't find shredded Swiss cheese and don't want to grate your own, substitute an additional cup of cheddar.
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