Butter an 11 x 8-inch baking pan or a casserole dish.
In a large bowl, toss together the steamed broccoli and the cooked pasta.
In a heavy-bottomed saucepan, heat the butter over medium heat.
Add in the onion; cook for about 3 minutes, or until softened.
Stir in the garlic and flour; cook for 1 minute.
Stir in thyme, then slowly whisk in the chicken broth and the half and half cream (or milk); add in the bay leaf and the 1/4 cup Parmesan cheese, bring to a medium boil, reduce heat; cook gently for 6-7 minutes, until mixture is thickened.
Add in the chicken pieces; cook for 2-3 minutes, until chicken is barely cooked through.
Remove from heat, season with salt, pepper and nutmeg.
Add the mixture to the bowl with the pasta/broccoli mixture, add in the chopped parsley; stir until mixed.
Transfer to prepared greased baking dish or casserole dish.
Dot with the cottage cheese.
Sprinkle with grated Parmesan cheese.
Bake for 20 minutes, or until heated through, and the top is lightly browned.