What to do with cooked mung beans?

http://www.banyanbotanicals.com/info/ayurvedic-living/living-ayurveda/diet/how-to-make-kitchari/
Here is a recipe you might try.

Indonesian Mung bean porridge! Something like http://indonesiaeats.com/bubur-kacang-hijau-indonesian-sweet-mung-bean-porridge/ ; just dump the cooked mung bean on pan, add sugar and water (in necessary) (see step 3), and finish the rest of the recipe.

Thanks, everyone! :) And hellooooooo GINGER: I love and miss you.

Not really relevant but one of Ginger's nicknames is "our little mung bean" - do not ask me why as I have no idea.

Julie Sahni's Whole Mung Beans and Spinach in a Spicy Tomato Butter (Palak Moong) from "Classic Indian Vegetarian and Grain Cooking". ;o)

Split mung beans or whole?

Either way, look into Vietnamese recipes. We like to put them into both savory and sweet dishes. For the sweet, make che dau xanh, which is a pudding like soup. Here's a recipe that you can jump into the middle since the mung beans are already cooked: http://runawayrice.com/desserts/sweet-mung-bean-pudding-che-tao-soan-che-dau-xanh/

You can use as a filling or an addition to the filling for Banh Xeo, the sizzling Vietnamese crepe filled with pork, shrimp, and/or split mung beans, like this one http://www.hungryhuy.com/banh-xeo-savory-vietnamese-crepes/

Or Banh Cong which is a fried shrimp and mung bean cake (more like a fritter), http://danangcuisine.com/recipes/recipe-fried-prawn-cake-banh-cong/

Google .... 101 cookbooks , a natural food journal. She has many recipes for mung beans

Depends on how you cooked it but Maangchi on youtube has several authentic Korean preparations.
Video for Mung Bean Pancakes (Bindaetteok) https://www.youtube.com/watch?v=QJJawgzmgOk
Video for Pan Fried Rice Cakes (Bukkumi): https://www.youtube.com/watch?v=ZFXIpaFWfSM
She also has several more.
I know Thai food also uses them in desserts mainly as garnish for mango with coconut sticky rice.

No idea, but here's what not to do with them: https://www.youtube.com/watch?v=fit7WFRb_iw (Sorry, my mind goes there whenever I hear "mung bean".)