Fill a small pot with water until about 3/4 full. Bring to a boil over medium-high heat. While water is coming to a boil, heat a large skillet over medium-high heat.
Add guajillo and arbol chiles to the skillet and toast, flipping occasionally, until fragrant and lightly toasted, about 1 minute. Transfer toasted chiles to a plate or bowl to rest until the pot of water is boiling.
Add toasted chiles to the pot of boiling water along with the roma tomatoes. Cover, lower heat to medium and simmer for 5 minutes.
Remove pot from heat and let it sit for 10 minutes to soften and rehydrate the dried chiles. While the chiles and tomatoes are soaking, heat olive oil in the same skillet over medium-high heat.
Add onions and garlic. Saute for 3-5 minutes until onions become translucent and have softened.
Transfer sauteed onions and garlic to a large blender. Then using a slotted spoon, add the soaked chiles and tomatoes as well. Add salt, oregano, and blend for 3 minutes, until completely smooth.
Carefully add blended sauce back to the same skillet (it may splatter, so be careful!) and cook for 1 minute over medium heat, stirring often.
Lower the heat to low. Use your large spoon to make 4 small wells in the sauce and crack an egg into each well.
Cover and cook for 7-10 minutes, or until the eggs are done to your liking.
Garnish with chopped cilantro, queso fresco, and serve with warm flour tortillas or crusty bread.
Notes
Adding chile de arbol peppers is optional. Only add them if you want to make the sauce a little spicy, or leave them out completely if you want the sauce very mild.
Huevos ahogados are best eaten immediately. If you do have leftovers, store them in an airtight container in the fridge for up to 4 days. You can reheat them in the microwave in intervals of 30 seconds to make sure the eggs don't get rubbery.