Pat the pork dry and season all over with the paprika and a big pinch of salt. Set aside.
Heat 2 tablespoons oil in a large cast-iron skillet over medium-high. Add the carrots, season with salt and stir occasionally until crisp-tender and charred in spots, 3 to 5 minutes. Turn off the heat. Scrape the carrots onto a plate and zest the lime over the top. Cut the lime in half.
Heat the remaining 2 tablespoons oil in the skillet over medium-high. Add the pork and the chiles. Cook, pressing the meat with tongs to prevent buckling, until browned, 3 to 4 minutes. Flip and cook until firm to the touch, 1 to 3 minutes. Transfer the pork to the plate (leave the chiles in the skillet).
Reduce the heat to medium-low and add the honey and juice from half the lime. Stir constantly until thickened and dark like maple syrup, 1 to 3 minutes. Turn off the heat, add the pork, carrots and any resting juices back to the skillet. Turn to coat in the glaze. Serve sprinkled with the cilantro.
