Rice Pudding

So I don't know what my issue is lately but I've been craving rice pudding like no ones business. I attempted a recipe I found around 11PM and it was awful and never thickened and didn't quite cook all the way. Good flavor but awful consistency.
SO! I had my sister dig through my mom's recipe cupboard and search for the best (in my opinion) rice pudding I've ever made.

2 ½ c.milk

2/3 c. min rice

1/4 c sugar.. + more

1 TB butter

1 tsp vanilla

½ tsp nutmeg

touch of cinnamon

drop of lemon extract

1/8 tsp salt

In a saucepan simmer on low-medium for about 6 minutes, stirring occasionally (be sure you don't burn the milk on the bottom of the pan)

Mix together:

<egg yolk

<2 Tb milk

Pour some of the hot milk mixture to the egg mixture, stirring together...

Beat the egg into the rest of the mixture and cook on low for 1 minute to thicken... 

Now the recipe says this:

Cook until rice is tender about 20 mins low heat...

Because that's how my mom cooks, not very specific and does it herself anyway!

So let it simmer, set on low... then remove from heat and let it stand for 20-30 minutes

Serve warm or chilled

(it's better warm, personally)

Enjoy!