Cut the scallions and chicken breasts into uniform 1½-inch pieces and skewer
Prepare the yakitori sauce: Place the soy sauce, sugar, mirin, scallion, garlic, ginger, and lemon zest in a saucepan and bring to a boil over medium heat.
Let the sauce simmer until thick and syrupy, 5 to 10 minutes, stirring often to prevent scorching.
Strain the sauce and let cool to room temperature. Set some aside to serve as a dipping sauce, if desired.
Place the yakitori at the edge of the hot grill so that the skewers are away from the heat. Grill the yakitori, turning after 2 minutes, to cook the outside of the meat.
Begin basting with the sauce, and continue basting and turning until the chicken is cooked, 3 to 4 minutes per side.
Alternatively, put the sauce in a shallow dish. When partially cooked, dip the yakitori in the sauce and continue grilling. The sauce should cook to a shiny glaze and the meat should feel firm to the touch when done.
Transfer the yakitori to plates or a platter and sprinkle with the scallion rings and sesame seeds. Although it’s not strictly traditional, I like to serve a little reserved glaze in a tiny bowl as a dipping sauce.
