Place thawed shrimp on a cutting board or plate and pat dry using a paper towel to remove as much excess water as possible.
In a food processor, combine the garlic, ginger, and red chilli and pulse until finely chopped, scraping down the sides as needed.
Add ½ of the shrimp to the food processor and pulse again until the shrimp is finely chopped.
Add remaining shrimp, green onion, cilantro, breadcrumbs, and salt and pulse a few times until broken down and pasty. Be careful not to over blend it, you still want some chunks of shrimp in there.
Once blended, shape mixture into 4 equal-sized burger patties.
Heat a grill or grill pan to medium-high heat. Brush the grill with a little bit of oil, add patties to the grill and cook for 4-5 minutes, flip and cook for an additional 3-4 minutes until cooked through. When the shrimp burgers are almost done, toast the buns on the grill or under the oven broiler on medium heat.
While the burgers are cooking, add the mayonnaise and sriracha to a small bowl and stir until well combined. Set aside.
In a medium bowl, add shredded cabbage, shredded carrots and cilantro, drizzle with rice wine vinegar, add a pinch of salt, and black pepper, and toss to combine. Set aside.
Once cooked, remove shrimp patties from the grill and assemble the burgers; add sriracha mayo to the bottom bun, add shrimp pattie to a bun, top with more sriracha mayo, a handful of the cabbage mixture, and the top bun.
Serve the burgers immediately; any leftover patties can be stored in an airtight container in the fridge for up to 3 days or in the freezer for 3 months.