Light a grill or preheat a grill pan; oil the grates or pan. In a small bowl, combine the black, white and cayenne pepper with 2 teaspoons of salt. Rub the pork with olive oil and pat the spice mixture all over it. Grill over moderately high heat, turning occasionally, until lightly charred and an instant-read thermometer inserted in the thickest part registers 135°, 8 to 10 minutes. Transfer the pork to a work surface and let rest for 10 minutes.
Meanwhile, in a medium bowl, whisk the lime juice with the 1/4 cup of olive oil and season with salt. Add the shallots and let stand for 5 minutes. Add the peach, cucumbers, mint and cilantro and season with salt. Slice the pork and serve with the salad, yogurt and naan.
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