I made the eggs the way my roommate does (and she makes the BEST egg sandwiches I've ever had) and then I put them in a warm corn tortilla and folded them over, empanada style. Finally I topped it with cilantro and pico de gallo. See the recipe and pictures below:
Eggs (1 egg per empanada)
6" CORN tortillas
Pico de Gallo
I use a small skillet to make the empanadas and do them one at a time
1. Heat skillet over Medium heat and use about 1/2 tbsp to coat the skillet
2. Crack the egg into the pan. Once the egg cooks for a few seconds (and white forms) break the yoke inside the pan. Let egg cook until the yolk is just cooked and sprinkle with pepper and hot sauce (to your taste).
3. Flip the cooking egg in half (or small enough to fit in one half of the corn tortilla) and flip so both sides are cooked. Top with shredded cheese (I used a 3 cheese blend of different Cheddars but you can use whatever cheese you like). Remove egg from skillet and set aside on a plate.
4. Add the corn tortilla to the skillet and flip so both sides are coated with the butter left in the skillet. Once it's soft and warm, place egg back onto one side of the skillet.
5. Next, flip the empty side of the tortilla over the half with the egg and press gently (the cheese should help it stick). Cook until empanada sticks and it's golden brown (or however you like it).
6. Finally, top with cilantro and pico and enjoy!
If you really want to give it a Mexican taste, you can use melted queso fresca drizzled on top. This is the closest thing I've found to the DELICIOUS breakfast I ate every day at a resort in Puerto Vallarta during spring break one year. It also gives a new twist to an egg sandwich or burrito.