Heat the oven to 200 C / 400 F. Line a sheet pan (33 x 46 cm / 13 x 18 inch) with foil or parchment.
Spread the tortilla chips in an even layer across the pan.
In a 1-quart / 1L saucepan, warm the black beans with cumin, chili powder and a pinch of salt over medium heat for 3 to 4 minutes, stirring, until heated through and any excess liquid has cooked off.
Scatter the warm beans over the chips, then top with the shredded cheddar. Bake for 6 to 8 minutes, until the cheese is fully melted and the chip edges start to brown.
While the nachos bake, heat the olive oil in a 10-inch nonstick or cast-iron skillet over medium-low heat. Whisk the eggs with salt and pepper in a mixing bowl, then pour into the skillet.
Scramble the eggs, stirring often with a wooden spoon, for 4 to 5 minutes, until the curds are soft-set and glossy with no runny liquid left. Pull them off the heat right at that point, they keep cooking on their own and turn rubbery if left too long.
Remove the nachos from the oven and immediately spoon the scrambled eggs over the top while everything is still hot.
Add the diced avocado, pico de gallo and dollops of Greek yogurt, then scatter the chopped cilantro over the top.
Squeeze fresh lime juice over the nachos, add jalapeno slices if using, and serve right away before the chips soften.