Combine masarepa, water, and vegetable oil in a medium bowl and knead with hands until a dough is formed. Take a small amount and flatten it between your palms. If the edges crack, knead in more water, 1 tablespoon at a time, until dough is supple and smooth but not sticky. Season dough to taste with salt.
Cover and set aside for 5 minutes.
Divide dough into 4 even pieces and roll into balls.
Flatten each ball down to a disk about 4-inches in diameter and 1/2-inch thick.
Melt butter in a 12-inch cast iron or non-stick skillet over medium-low heat.
Add arepas and cook, moving them around the pan and rotating them occasionally, until first side is charred in spots and a dry crust has formed, about 5 minutes. Flip arepas and cook on second side until a dry crust has formed, about 5 minutes longer.
Transfer to a baking sheet and bake until cooked through, about 10 minutes longer.
Remove from oven, let rest 5 minutes, split, fill, and serve.