Arrange the oven rack to the lower third position and preheat the oven to broil. Line a large baking sheet with parchment paper, aluminum foil, or spray with cooking spray.
Drizzle a tablespoon of olive oil in the bottom of a large skillet, like a cast iron skillet, over medium-high heat. When it’s hot, brown the sausage for 3-5 minutes, breaking it up into small pieces, until it’s fully cooked and no pink remains. Use a slotted spoon to transfer the sausage to a paper towel-lined plate. Drain the 1-2 Tablespoons of fat from the pan.
Whisk the eggs in a large bowl with a splash of milk or water, salt, and pepper.
Add the butter to the same skillet over low heat (Note 5). When the butter is melted, pour the egg mixture and let them cook for a few seconds without stirring. Use a rubber spatula or wooden spoon to push the eggs across the bottom of the pan to form scrambled egg curds. Continue cooking on low heat, folding and stirring the eggs every few seconds for 5-7 minutes, or until they’re almost cooked all the way. Remove the pan from the heat when the eggs are very soft with some remaining liquid. They will continue cooking in the oven and you don’t want to overcook them.
Arrange the tortilla chips on the prepared baking sheet in a single layer. Evenly distribute the cooked sausage and scrambled eggs over the prepared tortilla chips on the sheet pan. Sprinkle with black beans and cover with shredded cheese.
Broil in the preheated oven for 2-4 minutes, watching the nachos the whole time so they don’t brown. Remove them from the oven when the cheese is melted and a few spots on the cheese and chips start to turn golden brown.
Finish the nachos with fresh pico de gallo, sliced avocado, sour cream, jalapeño, red onion, or any other desired toppings. Serve warm right away.