If you prefer a leaner cut of meat, remove the thin layer of fat which would be crispy and a bit chewy after cooking. Salt half of the meat with half of the salt and massage well in order for the salt to penetrate.
Place in a plastic bowl and refrigerate for 4 hours on the bottom shelf of the refrigerator, which is less cold. Then remove the meat from the refrigerator and salt the other half of the meat (only the red areas) with the other half portion of fine salt.
Refrigerate again, but this time for 12 hours. Water will be drawn out of the meat. After this time, put just the meat in a plastic bag and freeze for 5 days.
Let the meat thaw completely in the refrigerator. Put the meat in a plastic bowl and fill with enough water to cover the meat. Leave for 30 minutes, drain the water and repeat the process twice more.
While the meat is being de-salted, de-salt the cheese as well in a separate plastic or ceramic bowl filled with enough water to cover the cheese. Let sit for 1 to 1-1/2 hours total, draining off the water and refilling the bowl with fresh water every 30 minutes during this period. Pat dry the cheese and reserve.
Pat dry the meat as well with a paper towel or a clean cloth. Divide the meat into 4 thick slices (cut across the grain of the meat) and then cut each of these slices in half so that they are in the form of large squares or cubes, trimming excess if necessary (these small meat trimmings can be cooked along with the other large pieces).
In a skillet over medium-high heat, melt half of the butter and then place the 8 large cubes of carne de sol into the skillet. Brown the 6 sides of the sliced carne de sol (about 1 minute on each side).
Pour the remaining half of the butter on top of the meat and finish cooking in a preheated oven at 350 degrees F (180 degrees C) for approximately 4 to 5 minutes (rare to medium) or for about 7 to 9 minutes (well done).
While the carne de sol is cooking, grill the slices of cheese on both sides in a greased cast iron grilling pan over medium-high heat. Once the meat is cooked, place on a plate and top each of the carne de sol cubes (steaks) with one slice of grilled cheese and serve immediately.
Once the meat is cooked, place on a plate and top each of the carne de sol cubes (steaks) with one slice of grilled cheese and serve immediately.