In a medium bowl, mix together the warm water, butter and salt. Place corn flour in another bowl, making a well in the center. Pour the liquid into the well, mixing with you hands until thoroughly combined. At first dough will stick to your hands; continue until it's soft and no longer sticky. Cover with a damp linen and allow the dough to rest for 10 minutes.
Separate the dough into 6 balls. Place the ball onto your palm, and flatten the ball into a disc, alternating between your two hand, that is 1/4-inch thick and 3-inches in diameter. To the center, add a tablespoon (you can eye ball this measurement) of mozzarella to the center. Fold in the sides until the mozzarella is no longer visible. And then gently form it into a 1/2-inch thick disc and press around the edges to eliminate any cracks.
Over moderately medium-high heat, brush the skillet with about the butter. Once the skillet is hot, add the arepas, being sure to not overcrowd the pan. Cook for 7-10 minutes on each side, until golden brown. Transfer the cooked arepas to a warm oven until you've gone through all 6.