Heat a large, heavy-bottomed skillet (preferably cast-iron).
Grab a small piece of pizza dough (about 1 tablespoon worth) and roll into a small ball. Dip into butter. Flatten out with your fingers into a tiny disk. Cook over high-heat, about 2 minutes per side, until toasted brown and cooked through. You may need to adjust the size of your little “naan” bites to ensure they cook through and are bite-sized.
Place naan on a serving platter. Top each with 2 to 3 leaves of cilantro, a slice of cheese, a dab of chutney, and a few cucumber matchsticks. Serve cold or room temperature.