Preheat the broiler. Line a baking sheet with parchment. In a medium bowl, whisk together 1/2 cup salsa and 2 tablespoons olive oil; season with salt and pepper.
In a small bowl, mash half of the black beans with the remaining 3 tablespoons salsa.
Arrange the tortilla chips on the prepared pan and top with the mashed beans and the cheese. Broil until melted, about 3 minutes.
In a bowl, toss the lettuce and remaining black beans with the salsa. Divide the tortilla chips among 4 plates; top with the salad.
In a large nonstick skillet, fry the eggs in the remaining 2 tablespoons olive oil over medium-high heat. Place an egg on top of each salad.