1.Using a vegetable peeler, slice carrot lengthways into thin strips. Cut carrot strips to width of beef.
2.Boil, steam or microwave asparagus until just tender; drain. Rinse under cold water, drain. Cut asparagus and onions to width of beef.
3.Place beef slices flat on work surface; sift half the cornflour over top of beef. Place two pieces of carrot and onion, and one piece of asparagus across dusted side of each slice of beef; roll up. Tie rolls with kitchen string or secure ends with toothpicks. Dust with remaining cornflour.
4.Heat oil in medium frying pan; cook rolls, in batches, until browned all over. Remove from pan.
5.Return rolls to same cleaned pan, add combined sugar, mirin, sake and sauce; bring to the boil. Reduce heat; simmer, turning occasionally, until rolls are cooked through. (If you prefer a thicker sauce, remove rolls; boil sauce until reduced. Return rolls to pan; turn to coat in sauce.)
6.Remove rolls from pan; cool 2 minutes. Discard string or toothpicks; cut rolls in half. Serve with sauce.
Very thinly sliced beef, sold as yakiniku or sukiyaki beef, is available from Asian grocery stores. You could use rib eye steak (scotch fillet) instead of the beef eye fillet. Pork fillet can be used instead of beef eye fillet, if you like. To make larger rolls, use two or three slices of meat, slightly overlapping.