Not for nothing are Mexicans known to be witty and sarcastic during life's downturns. Consider the name given to these eggs: "divorced." They are perfect for people who can't decide between red sauce and green sauce, or for voracious types like me, who want them both at the same time.
Eat these eggs for breakfast, for lunch, or at 2 a.m.., but eat them. Traditionally the eggs should be served sunny-side up so the yolks break into both sauces and turn the divorce into an even bigger mess.
<p><strong>*Note:</strong> I like my eggs with the whites cooked and the yolks still runny. I crack the eggs into the hot skillet and then cover with a lid or a plate to let the steam help cook the whites from above.</p>
Heat ¼-inch oil in a medium-sized skillet over medium-high heat until hot but not smoking. (The oil is ready if the edge of a tortilla dipped in creates bubbles around the edges without going wild.) Line a plate with paper towels.
Using tongs, dip the tortillas one at a time in the oil for 10-15 seconds per side. The tortillas will first appear to soften and then begin to crisp. Drain on paper towels and cover with aluminum foil or an inverted plate to keep warm. (As an alternative, you can lightly toast the tortillas on a well-heated comal or in a skillet over medium heat for 30 seconds per side.)
Pour off all but 2 tablespoons of the oil. Heat the oil over medium heat. Crack 2 eggs into the pan, season with salt, to taste, and cook to the desired level of doneness.* Keep warm while you repeat with the remaining eggs.
To serve, place 2 of the warmed tortillas on 4 plates and top with 2 eggs. Ladle a generous amount of salsa verde over 1 of the eggs on each plate and red sauce over the other. Serve with the refried beans on the side and cheese on top.