Smoke jalapeños and poblano peppers at 225 degrees Fahrenheit for 3 hours. Pull and seed the poblanos, then set aside.
Cut off the stems of jalapeños and add to the stemless peppers to a food processor, along with all the other ingredients for special mayo (besides the mayonnaise). Blend thoroughly, then add the mixture to a large mixing bowl and add the mayonnaise. Thoroughly hand mix. Set the special mayo aside until you are ready to serve.
Grind the wild turkey meat through a fine die. Make sure to remove the tendons before grinding. Mix the ground turkey with mayo, fish sauce, granulated garlic, ground ginger, and paprika. Form the meat mixture into four patties.
Skin the mangoes. Thinly slice the mangoes and red onion.
Preheat the oven to 450 degrees Fahrenheit. Cut the stems off the greens and lightly oil the leaves. Toast the leaves in the oven and remove them once they’re slightly charred (about 5-10 minutes).
To cook the turkey burgers, in a large skillet, heat half an inch of peanut oil to 375 Fahrenheit. Do not crowd the pan, so only fill the skillet half full. Add the patties to the oil to cook. Flip once the underside is golden brown, approximately 3-5 minutes. Add a generous amount of freshly sliced mango and one poblano to each patty, top with cheese, and cover skillet if necessary. Cook for another 3-5 minutes, or until the cheese is melted and the burger is fully cooked to 160 F.
To serve, toast the buns and add a healthy amount of special mayo to each side. On the bottom bun, add the toasted greens, followed by the burger, then a layer of sliced red onions, and then the top bun. Enjoy!