Peel and cut the carrot into 3" long (7.5cm), 1/3" (8mm) square sticks. Cut green beans into 3" long pieces.
Cook carrot first in salted boiling water for 2 minutes, and add green beans and cook together for another 2 minutes. Strain and let them cool.
In a small bowl, mix Soy Sauce, sugar, Sake, and 2 Tbsp water until the sugar dissolves completely. Set aside.
Open up a thin beef strip on a cutting board, place 2-3 carrot sticks and 2-3 green beans on the end of the meat, and then roll up. Repeat for each strip of meat.
Heat oil in a frying pan at medium heat, place the meat rolls in the pan (end of the meat strip down), and start cooking. Cook while turning, until browned all the way around, about 7-8 minutes.
Turn down heat to low, and add Soy Sauce mixture. Coat the meat with the sauce well.
Cut the rolls in half, and serve.