Heat the oil in a large skillet over medium high heat until shimmering. Add the corn tortillas, 2 at a time, and fry for 60 to 90 seconds on each side until golden brown and crisp. Remove the tortillas from the oil and transfer to a paper–towel lined plate to dry. Repeat this process for the remaining tortillas.

Once the tortillas have been fried, drain the oil from the skillet and put the butter into the skillet to melt. Carefully crack 3 eggs in the skillet, evenly spaced so they have room to cook, and cook until the egg white is solid, 3 to 4 minutes. Remove the fried eggs from the skillet and lay each one onto a tortilla. Repeat this process for the remaining 3 eggs.

Cut the avocado in half lengthwise. Remove the pit from the avocado and discard. Remove the avocado from the skin, and place the avocado on a cutting board. Cut 6 thin slices from each half of the avocado and transfer 2 slices on top of each fried egg.

Sprinkle the queso fresco on top and season with salt and pepper if desired. Serve immediately.