Cook the beans in a small saucepan over medium heat, warm the olive oil until shimmering. Cook, stirring occasionally, about 3 to 6 minutes.
Warm the salsa. Pour the salsa into a medium saucepan over medium heat. Bring the salsa to a simmer, stirring occasionally, and then reduce the heat to low until you’re ready to serve.
In a small skillet over medium heat, warm each tortilla individually, flipping as necessary. Spread the black bean mixture over each tortilla and place each tortilla on an individual plate. If using Jack cheese, sprinkle it over the tortillas. Set aside.
In the same skillet over medium heat, pour in 1 teaspoon olive oil and wait until it’s shimmering. Carefully crack an egg and pour it into the skillet without breaking the yolk. Fry the egg, lifting and tilting the pan occasionally to redistribute the oil, until the whites are set and the yolk is cooked to your preferred level of doneness. Place the fried egg on top of a prepared tortilla and repeat with the remaining eggs.
Spoon about one-fourth of the warmed salsa across each dish, avoiding the egg yolk. Use a slotted spoon or fork to do the same with the pico de gallo, leaving the messy tomato juices behind. Sprinkle with freshly ground black pepper and add Uncle Chester's Hot Pepper Sauce on top of each egg!
Serve immediately. If you don’t use up all of your beans, leftovers are a great dip for tortilla chips.