This sounds very similar to what my Chinese friend makes. She calls her congee.
Yes, its called congee or rice porridge in Asian countries. Its usually plain cooked rice with extra water and topped with variety of ingredients. Some of the toppings I have tried are;
Scrambled egg, spring onion, fried anchovies, seaweed, tofu, cooked beans, chillies, peanuts, sweet corn, silver fish, sliced fish, cooked minsed chicen and a few more which I can't remember now.
For my kids I used to give them this once or twice a week with some minsed meat and spinach which they loved, the sweet version I make will be with sugar (brown/white/orange), butter and cashew nuts......H loves it!
Its a staple dish for chinese if I am not wrong and they traditionally eat it with steamed fish and salted vegetables(correct me if I am wrong) which I have tried too.
Hmmm...talking about this food, I feel like eating this right now with scrambled egg, anchovies and chilli...Yum!