In a large mixing bowl, gently combine ground turkey, breadcrumbs, green onions, cilantro, garlic, ginger, soy sauce, lime juice, sesame oil, salt, and black pepper until just incorporated. Don't overwork the meat.

Divide the turkey mixture into four equal portions and form into uniform patties, about 3/4-inch thick. Make a slight indentation in the center of each patty.

Heat a grill or skillet over medium-high and lightly oil the surface before cooking.

Grill or pan-cook patties for 5 to 6 minutes per side until fully cooked with an internal temperature of 165°F.

Rest patties for 3–4 minutes after cooking to retain juices.

For oven-baking, preheat oven to 400°F, place patties on a parchment-lined tray, and bake for 18–22 minutes, flipping halfway through.

In a separate bowl, whisk together peanut butter, soy sauce, lime juice, honey, and sriracha. Gradually blend in warm water until smooth.

Spread peanut sauce on the bottom of each toasted bun, place a turkey patty, drizzle with more sauce, and top with carrot, cucumber, cilantro, and red onion. Cover with the top bun and serve immediately.