How to Make It
Place the chiles in a saucepan with enough water to cover and bring to a rolling boil (this can be done in batches). Cook them for about 5 to 10 minutes, checking frequently, or until they're soft but not dissolving. (If you'd like to make a milder version of the dish, remove the seeds from the puya chiles, which give the dish its heat.)
Once the chiles have softened, remove them from the water and leave them to cool before puréeing in a food processor. Use some of the reserved water as you go. The consistency should be something like a thick tomato soup.
When the chiles are thoroughly blended (if you want this to be really fine, you can put it through a strainer to remove any remaining chunks of seeds), add the onion and garlic, and continue blending until smooth. Remove from the processor and set aside in a large pot.
Boil and peel the tomatoes, then blend them to a liquid, adding as much water as you need to reach a similar texture to the chile mixture. Once blended, add the tomatoes to the pot with the chile mixture and bring the whole thing to a boil. Add salt and as much water as you like to reach the desired texture, which can be very soupy or slightly thicker, if you prefer. Leave at a gentle boil for 15 to 20 minutes, stirring to make sure it doesn't burn and checking for taste as you go. If it's too spicy, add water. If it's not flavorful enough, add salt. Also, add a couple tablespoons of oil.
As the sauce comes to a boil, whisk the eggs together in a bowl and season with salt and pepper. Using a pan of desired size (a 12-inch skillet should do), add plenty oil and fry eggs into a few omelets—similar to a Spanish torta—roughly a half-inch thick. Use as much oil as necessary to make sure they flip easily in the pan (the excess oil will go into the sauce, so it's OK). Once the omelets are made, set them aside and allow them to cool slightly before cutting them into quarters.
In the last couple minutes of the sauce cooking, add the epazote (if you found it) it to the soup and allow it to cook. Once the herb has become aromatic, add the omelet wedges and lower the heat to a gentle boil, and leave it cook long enough to make the eggs hot again. Once it's all at a consistent temperature, remove from heat and serve with tortillas, beans, or rice.