Twin Chicken and Broccoli Casseroles

2 teaspoons vegetable oil2 pounds boneless, skinless chicken-breast halves1 medium onion (for about 3/4 cup chopped)1 box (10 ounces) frozen, chopped broccoli1 bag (16 ounces) frozen broccoli cuts (see note)2 large eggs1 can (10 3/4 ounces) 98 percent fat-free cream of mushroom soup1 cup already shredded sharp cheddar cheese1 cup already shredded Swiss cheese 1/2 cup reduced-fat mayonnaiseCooking-oil spray1 cup butter cracker crumbs, such as reduced-fat club crackersHeat the oven to 350 degrees. Spray two 1 1/2-quart casserole dishes with cooking-oil spray.Heat the oil in a 12-inch skillet on medium. Dice the chicken breasts into 1/2-inch pieces, and add them to the skillet. When all the chicken is added, raise the heat to medium-high. Peel and chop the onion, adding it to the skillet as you dice. Stir and cook the chicken and onion until the chicken is just cooked on the outside, about 4 to 5 minutes. (The chicken will cook through in the oven.) Set aside.Place the 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 the mushroom soup, cheeses and mayonnaise. Stir well. Press the broccoli with the back of a spoon to remove as much water as possible. Add it to the bowl. Add the reserved chicken and onions, and stir well.Pour the broccoli and chicken mixture evenly into each dish, and smooth each with the back of a spoon. 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.Do-ahead tip: The casseroles may be refrigerated for three days or frozen up to one month after they are baked. 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 20-30 minutes covered with aluminum foil until heated through. Uncover for the last 5-10 minutes to crisp the crumbs.Each casserole serves four.Cook's notes: This recipe uses two types of broccoli. The broccoli cuts (smaller pieces than florets but not quite as fine as chopped) add texture, while the chopped broccoli is a necessary binder. If you can't find frozen cuts, substitute florets or spears, and chop them 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.Nutrition values per serving: 439 calories, 20 g fat (8 g saturated), 23 g carbohydrates, 3 g fiber, 37 g protein, 148 mg cholesterol, 770 mg sodium.