Rice in Parmesan Sauce with Broccoli

This recipe has become one of our go-to dishes when there is not much food in the house.  I do the grocery shopping and to make $30 stretch for a week we buy a lot of basics to make many things out of--in this case butter, milk, rice and frozen vegetables.  I love frozen veg because it lasts forever and when it goes on sale it is super cheap.  It also takes less than 15 minutes to make in total so it's easy too.
We always buy brown rice, going through enough that I have to buy a big bag almost every week.  Rice is great because it is one of those things you put on the stove and then just leave for an hour or so, leaving you free to do other things.  Brown rice is super healthy, and (in my humble opinion) far tastier than the white stuff.
The key to this recipe is the white parmesan sauce.  I was always terrified of making white sauce because my mother warned me growing up of how important it is to constantly stir or it will go wrong.  When I finally bit the bullet and tried it for myself, though, I found that it was shockingly simple.  It's not exactly the healthiest addition to any meal, but I make it with skim milk and it works just fine and still tastes creamy.  It's also spectacular because of how flexible it is--you can add just about anything to it to make it perfect for just about any meal.  In this case we added parmesan cheese, salt and pepper.
A note: for recipes like this I just eyeball lots of the ingredients, so the amounts here are approximations.  Feel free to play!

Rice in Parmesan Sauce with Broccoli (serves 2 as main dish or 3-4 as a side):


1 cup rice
2 cups water
1 1/2 cups frozen broccoli
1 cup milk
2 tbsp butter
2 tbsp flour
1/2 cup grated parmesan cheese
salt
pepper

Put one cup of rice and 2 cups water in a small pot.  Heat on medium-high until you can hear it boiling--about 7 to 10 minutes--and then leave on low heat for about 40-50 minutes more.  Put the frozen broccoli in another pot with just enough water to almost cover it and cook on medium-high heat for 10-15 minutes, or until cooked.  Drain and then chop into smaller pieces.  Set aside.  (It's okay if it gets cool--the parmesan sauce will keep everything nice and hot.)
About 20 minutes before the rice will be done, melt the butter in a small saucepan.  Whisk in the flour and continue whisking until bubbling.  Remove from heat and add milk, mixing thoroughly.  Return to low-medium heat and stir constantly until bubbling.  Let simmer (while stirring!) for 1-3 minutes, or until the sauce thickens.  Remove from heat and stir in parmesan cheese, salt and pepper to taste.
Mix rice, parmesan sauce and chopped broccoli together.  Serve while warm.