In a large bowl, mix the masarepa with the melted butter, milk, and salt. Stir to combine and allow to sit for 5 minutes before stirring again and using.
Form small patties from the dough.
Preheat a cast iron pan to medium high heat with a splash of oil coating the bottom. Cook the arepas in the pan to char on both sides and cook through. Remove from heat and allow to cool
Mash the avocado in a bowl with the garlic, lime, and a pinch of salt.
Form the beef into 8 equal sized meat balls. Season the outside of the balls with salt and pepper.
In the same pan with a little more oil, in batches of needed, add the meat. Cook on one side for 3 minutes then flip. As you flip, use the spatula to smash them ball as flat as you possibly can.
After 2 minutes, flip and top with cheese.
Meanwhile, use a knife to split the arepa half way. Spread avocado on the bottom.
Double up the burgers in the pan, then transfer to the arepas. Top with more avocado and the cilantro and serve.