Preheat oven to 375F/190C.
Spray a 9" x 13" casserole dish with olive oil or non-stick spray.
Dice up a small onion, heat olive oil in a large frying pan (big enough to hold all the ingredients), and cook the onion over medium-high heat until it's starting to slightly brown.
Add minced garlic and cook 1-2 minutes more.
When onion and garlic are cooked, add Alfredo sauce, poultry seasoning, ground thyme, Spike Seasoning, black pepper, and sour cream to the frying pan. Stir to combine and let the mixture start to simmer over low heat.
Cut up rotisserie chicken (or chicken breasts you cooked yourself) and add to sauce mixture. Simmer about 5 minutes.
Cut up broccoli into bite-sized pieces, put in bowl (or large 8 quart glass measuring cup) and microwave the broccoli 1-2 minutes, depending on how cooked you like it.
Gently stir the cooked broccoli into the chicken and sauce mixture.
Add 1 cup of grated Swiss cheese, and gently mix the cheese in.
Then transfer the chicken-broccoli-sauce mixture to the casserole dish
Top with the rest of the Swiss cheese and the Parmesan cheese.
Bake 25-30 minutes, or until the mixture is bubbling hot and starting to brown on top.
Serve hot.
This will keep in the fridge for several days. It's also not bad when it's been frozen, thawed, and reheated, although the broccoli will get a little softer after it's been frozen.
