In a large bowl, combine the ground turkey, chopped scallions, minced ginger, honey, curry powder, cinnamon, 1 teaspoon kosher salt, and 1/2 teaspoon black pepper; mix gently until just combined.
Form the mixture into four even patties, cover, and refrigerate while you prepare the dill-yogurt sauce, or chill for 2 to 12 hours if time allows.
In a small bowl, whisk together the soy sauce and Worcestershire sauce; set aside for basting.
Make the dill-yogurt sauce by whisking together the Greek yogurt, chopped dill, lemon juice, pressed garlic, 1/4 teaspoon kosher salt, and a pinch of black pepper; cover and refrigerate until serving.
Heat a gas or charcoal grill to medium-high heat and lightly spray or oil the grates.
If using, butter the cut sides of the brioche buns and set them aside to toast on the grill later.
Place the turkey patties on the grill over direct heat and brush the tops with the soy–Worcestershire mixture; cook for about 7 minutes.
Carefully flip the patties with a spatula, brush again with the basting sauce, and continue cooking while you place the pineapple slices on the grill.
Grill the pineapple slices about 3½ minutes per side, flipping once, and cook the burgers until they reach 160–165°F internal temperature, about 7–8 minutes total; remove burgers and pineapple when done.
Place the buns cut-side down on the grill and toast for 1–2 minutes until lightly browned and toasty; remove from the grill.
Assemble each burger by spreading about 1 tablespoon of dill-yogurt sauce on the bottom bun, adding lettuce, the turkey patty, a grilled pineapple slice, and the top bun; serve immediately.