In a bowl, combine the radishes, carrots, jalapeno, rice vinegar, and coconut aminos with a little salt and pepper. Toss to coat and set aside or refrigerate until ready to serve while you prepare your burger.
Combine all of the aioli ingredients in a bowl, Stir to combine and refrigerate until ready to serve.
In a bowl, combine all of the "for the burger" ingredients in a bowl and mix using your hands until just combined.
Form into two large patties (or make 4 smaller patties if you prefer).
Grill until cooked through, pork should register at 160 degrees when reading with a thermometer. If you want to cook them on a cast iron: Heat over high heat and sear each side of the burger until golden brown, about 3 minutes per side. Reduce heat to low and cover and continue to cook until pork is cooked through, about 7-10 minutes covered on low.
For serving, fill your plate with lettuce, cucumbers, avocado, fresh mint, cilantro, and basil, and serve with the pickled veggies and a wedge of lime. Top with aioli! Enjoy!