In a medium non-stick skillet heat the butter over medium heat. Add the ham and cook about 2 minutes, stirring occasionally.
Meanwhile, in a small bowl beat the eggs, heavy cream, salt. and pepper. Pour the eggs in the skillet with the ham and cook over medium heat, without stirring, until mixture begins to set.
Stir twice or until the eggs mix with the ham and cook about 2 minutes or until the eggs are the consistency you like.
Place the arepas on a baking sheet and top with the eggs. Scatter the cheese evenly over the egg, leaving a ½-inch border. Slip under the broiler about 4 inches from the heat source and broil until the cheese is melted, about 2 minutes.
Arrange the tomato slices, avocado and cilantro on top. Season with salt and pepper, and serve immediately.