Step 1

Preheat grill to high (see cook's note if using charcoal). Cover onion with cold water and let stand 10 minutes; drain and pat dry. Mix together turkey, ginger, garlic, soy sauce, and sesame oil. Shape into four 4-ounce patties, then flatten each to 1 inch thick and season with salt. (Patties can be made a few hours ahead and refrigerated.)

Step 2

Brush grates with vegetable oil. Grill pineapple until lightly charred on both sides and softened, 4 to 5 minutes. If desired, grill split sides of buns until lightly charred, about 30 seconds.

Step 3

Grill patties until slightly charred and just cooked through, 6 to 8 minutes a side. In last minute of cooking, top each patty with cheese, cover grill, and let melt.

Step 4

Stir together mayonnaise and jalapeño. Spread buns with mayonnaise mixture and use to sandwich patties, pineapple, lettuce, and onion.