Wash and scrub the potatoes thoroughly. Pierce each potato several times with the tip of a knife.
Wrap the potatoes in damp paper towels and place them on a microwave-safe plate. Microwave in 3-minute intervals, checking after each interval. Remove individual potatoes as soon as they are tender but still firm. Depending on their size and microwave power, this may take around 9–12 minutes.
Carefully cut the hot potatoes into bite-sized pieces.
Heat the oil in a large cast-iron or heavy skillet over medium heat. Test with one potato piece; it should sizzle immediately when the oil is ready.
Add the potatoes in a single layer and leave them undisturbed for approximately 3 minutes. Turn the pieces to expose another side to the hot skillet.
Add the chopped onion and cook for another 3 minutes. Continue turning the potatoes occasionally for about 5 minutes, until crispy and golden. Season with salt and pepper.
Transfer the potatoes to a paper towel-lined plate or tray to drain any excess oil.
Meanwhile, combine the drained black beans and 1 cup salsa in a small saucepan. Cover and cook over medium-low heat for approximately 5 minutes, stirring occasionally, until bubbling and thoroughly heated.
Crack the desired number of eggs into a bowl and whisk until combined.
Heat a nonstick skillet over medium heat. Add approximately 1 tablespoon butter for every 2 eggs.
Once the butter has melted, pour in the eggs. Use a silicone spatula to gently pull the eggs toward the center as they cook. Continue until softly scrambled and just set.
Turn off the heat and sprinkle grated cheddar cheese over the eggs. Allow the residual heat to melt the cheese.
Assemble each Southwest Breakfast Bowl with crispy potatoes, salsa black beans, cheesy scrambled eggs, and sliced avocado.
Finish with chopped cilantro and additional salsa. Serve immediately.