Combine rice and 2 cups water in medium saucepan. Bring to a boil. Cover and simmer about 55 minutes until almost all water is absorbed and rice is tender. Add grated squash and cook 10 minutes more. Remove from heat. Add onion and cilantro, salt to taste.    

In medium frypan, heat 1 tsp oil- add one tortilla.  Top with 1/4-1/3 cup of rice mixture. Top with 1/3 of cheese then another tortilla. Cook until browned then flip and cook other side until browned.  

Cut each quesadilla into 8 wedges and serve immediately.