Preheat grill to medium high heat. Brush the grates with oil.
To make the teriyaki glaze, combine soy sauce, brown sugar, honey, mirin, ginger, and garlic in a small saucepan. Bring the mixture to a simmer over medium heat and allow to simmer for about 15 minutes.
Dissolve cornstarch in cold water then whisk mixture into soy sauce mixture. Continue to simmer another 5-10 minutes, whisking occasionally, until sauce is thickened (it should coat the back of a spoon). Remove from heat and set aside.
Toss beef strips with sesame oil in a large bowl then thread onto skewers. Season generously with salt and pepper.
Place skewers on the prepared grill. Cover and grill 5 minutes on each side. Brush generously with teriyaki sauce then grill another 4 minutes or until glaze is somewhat "set."
Serve skewers with rice and extra teriyaki sauce.