For the glaze, heat the oil in a heavy medium saucepan over medium-high heat. Add the ginger and garlic and sauté for 2 minutes. Add the tamarind concentrate, honey, Sriracha, and water and bring to a boil. Reduce the heat and simmer the mixture until it is thick enough to coat the back of a spoon and reduced to about 1 cup, stirring often, about 8 minutes.

Let the glaze cool completely, then mix in the lime juice.

Prepare a charcoal fire or gas grill to medium heat or place a grill pan over medium- high heat and coat it with cooking spray or oil. A nonstick or cast- iron pan is also fine for cooking these.

For the burgers, mix together the mayonnaise, ginger, salt, pepper, cumin, jalapeño, cilantro, and 4 teaspoons of the glaze in a large bowl, then mix in the scallions. Add the ground turkey and mix it well but loosely with the mayonnaise mixture; do not overwork. Shape the turkey into eight ½- inch- thick patties (or smaller ones for little people).

Grill the rolls, cut side down, until golden, about 2 minutes; transfer them to a serving platter. Grill the burgers until cooked through and a thermometer inserted into the center registers 160 degrees, about 8 minutes on each side. Brush each burger with the remaining glaze and serve with garnishes, and a spread of your choice for the buns— I like mayonnaise spiked with a drop or two of Sriracha.