Preheat a grill to medium-high heat (about 400°F/200°C).
In a large bowl combine the ground turkey, minced garlic, chopped jalapeño, 1/2 cup of the shredded cheddar, panko, 2 tablespoons minced cilantro, and kosher salt; mix gently until just combined.
Divide the mixture into 4 equal portions and shape each into a patty about 3/4–1 inch thick.
Place the patties on the preheated grill and cook until fully cooked through, about 10 minutes total, flipping once halfway through.
While the burgers cook, place the peach slices on the grill and cook until slightly softened and charred, about 4–5 minutes total, flipping once.
Just before removing the burgers from the grill, divide the remaining shredded cheddar among the patties and close the lid briefly until the cheese melts.
Make the cilantro-lime aioli by whisking together the mayonnaise, lime juice, lime zest, and 1 tablespoon minced cilantro; keep cold until serving.
To assemble, place each cheeseburger on a toasted bun, top with grilled peach slices and reserved cilantro, and spread with the cilantro-lime aioli.