Melt half the butter in a pan on medium heat, then throw in the potato and cook for 5 minutes, stirring minimally. Season with salt and pepper. Add the mushrooms and garlic, as well as a splash of water if the potatoes are getting stuck to the pan. Cook for another 5 minutes, until the mushrooms are brown and have shrunk down.
Test the potato by piercing one piece with a fork. If it goes through easily, you’re done. If not, cook for a few more minutes. (The smaller the potatoes are chopped, the quicker they’ll cook.) Taste and adjust the seasoning to your preferences.
Melt the other teaspoon of butter in another pan on medium heat. Crack the eggs into the pan and dust with salt and pepper again. Salt and pepper are critical to these ingredients, so don’t worry about overdoing it.
If you like your eggs sunny-side up, place a lid over the pan to ensure the whites will cook through without making the yolks hard. Once the whites are no longer translucent, take them off the heat.
If you like eggs over-easy (my favorite), wait until the yolks are cooked but still look runny, then flip each egg with a spatula and let the other side cook for about 15 seconds. That’ll get your whites fully cooked, but keep the yolks runny—the best. If you prefer hard yolks (please no!), then cook for a little longer.
Toast the bread or bun, then assemble it into a sandwich, using any condiments you like. Way better than what you’ll find at the corner deli.