Heat butter in a saucepan over high heat. Cook onion and garlic for 1 minute. Cook the chicken until it turns pink to white.
Turn the heat down to medium. Mix flour with the water and continue stirring for about 1 minute.
Mix half of the milk into the flour, stirring constantly. Once the flour is incorporated, add the remaining milk to the bowl and stir.
Add broth, rice and thyme to the pot. Season with a pinch of salt and pepper.
Mix, reduce heat to low, and cover. Reduce heat to medium low, and let cook for 12 minutes.
Take off lid. There should be liquid at the surface. Add the broccoli quickly. Push it down until it is partially submerged. Cover and continue cooking for 3 minutes more, or until the broccoli is cooked.
Preheat grill/broiler. Turn off the lid and mix half of the cheese. Don't worry about it looking a little too saucy. The excess liquid will evaporate in a matter of minutes . Smoothen the surface and top it with the remaining cheese. Broil or grill until the cheese is melted. Or, you can place a lid on the pan and let it melt on the stove.
Serve immediately garnished with parsley, if desired