Heat beans and milk in a small saucepan on low heat; stir occasionally.
Set oven to lowest temperature, and place a plate in the oven. Heat a teaspoon of olive oil in a large skillet over medium heat. Heat tortillas, one at a time, for a minute or so, until tortillas are soft. Add more oil as needed between tortillas. Place heated tortillas on plate in oven to keep warm.
Add tomatoes to warm skillet. Bring to a boil; turn down heat to a low simmer.
Heat another large skillet over low. Add a bit of butter; add eggs, one at a time. Cook to desired doneness of eggs.
Spread beans evenly among 6 tortillas. Top with one egg; top evenly with tomato mixture. Sprinkle evenly with queso fresco and cilantro.