To prepare the pickled vegetables, in a medium mixing bowl, stir together the radish, carrots, vinegar and sugar. Cover the bowl and let the mixture marinate at room temperature for 15 minutes. (This can be made up to one day in advance and stored, covered, in the refrigerator.)
While the vegetables are marinating, prepare the turkey burgers. In a medium mixing bowl, combine the meat, Sriracha, cornstarch, fish sauce, garlic, basil and some salt and pepper. Divide the mixture into four equal portions and shape each portion into a burger. Place a large skillet over medium heat with the sesame or vegetable oil and cook the burgers, flipping once, until cooked through, 4 to 5 minutes per side.
While the burgers are cooking, prepare the Sriracha mayo. In a small bowl, stir together the mayonnaise and Sriracha. Set aside.
To serve the burgers, divide the Sriracha mayo among the four rolls. Top with a burger patty, a scoop of pickled vegetables, 4 to 5 sprigs of cilantro and some sliced jalapeno (if using).
You can use whatever type of meat you like to make this burger. Lighter meats - like turkey, chicken and pork - will carry the flavors of the sandwich better than ground beef.