Glaze is what defines the teriyaki hot sando. It takes the sealed-pocket format from the baseline hot sando and fills it with teriyaki chicken: pieces of chicken cooked in the soy, mirin, and sugar sauce that reduces to a dark, sticky, sweet-salty lacquer. Of all the savory builds in this family, this is the one where the filling is defined by a sauce that is already concentrated and clinging rather than loose, which changes how it behaves once the plates close over it.
The technique centers on managing that sticky glaze and the chicken's own moisture. The teriyaki should be reduced until it coats the chicken and stops short of pooling, because a thin runny glaze will soak the crumb and a too-wet one will steam the bread limp from inside. The chicken is usually thigh, sliced or chopped so it lies flat and warms evenly, kept short of the crusts so the press can still weld the edges. Many cooks add a layer of cheese or a little Japanese mayonnaise, which moderates the sweetness and binds the filling so the cross-section holds together. Under heat the glaze goes glossy and almost candied at the edges where any of it meets the hot bread, and that faint caramelized note against the toasted shokupan is the signature of a good one. The failures are specific to this filling: an underreduced sauce that turns the inside soggy and one-note sweet, or scorching because the sugary glaze that escaped the seal burned against the iron faster than plain bread would. The chicken must be hot through and the glaze clinging, not swimming.
Variations work the sweet-savory balance. A sharper cheese or a handful of raw onion or scallion cuts the sugar; a dab of wasabi mayonnaise pushes it the other way; some builds add lettuce after pressing for a cold crunch against the warm filling, though lettuce inside the press wilts to nothing. There is also a version built on chicken katsu glazed with teriyaki, where a fried cutlet changes the texture entirely, and that combination is enough of a distinct experience that it deserves its own article rather than being crowded in here.