The most amazing rice pudding on the planet

I found this recipe on Allrecipes and modified it just a bit.

3/4 cups uncooked white rice

2 cups milk, divided

1/3 cup white sugar (heaping cup)

1/4 tsp salt (I used sea salt)

1 egg beaten

1 Tbsp Butter

1/2 tsp vanilla ( I don't measure vanilla but if I had to guess, I used about 1 tsp or more)

Cook rice and 1 1/2 cups water covered for about 20 mins

combine cooked rice, 1 1/2 cups milk, sugar and salt. cook until thick and creamy about 20 mins.Stir in 1/2 cup milk and beaten egg, stirring constantly for 2 mins. Remove from heat and mix in butter and vanilla. Pour in bowl and serve warm. I sprinkled a mixture of sugar, cinnamon and nutmeg on the top of the pudding. YUMMMY