Melt the butter in a wide pot over medium heat. Add the onions and cook, stirring only occasionally, until they are soft and deeply browned, 30 to 45 minutes. If the onions start getting too dark, turn the heat down to medium-low. Add salt and pepper to taste.
Once the onions start cooking, put the steak in the freezer for 30 minutes. This makes the meat easier to slice thinly. Once it’s out of the freezer, slice the meat as thinly as possible.
Put the sliced steak in a large bowl and toss lightly with a little bit of olive oil and generously season with salt and pepper. Set aside.
In a wide skillet, heat 3 tablespoons of olive oil over medium heat. Add the mushrooms and cook for 5 minutes. Add the peppers and cook the mushrooms and peppers until tender, 10 to 20 minutes more. Add salt and pepper to taste.
Heat a skillet (ideally, cast iron) over high heat. When it’s hot, add the pieces of steak, cooking for only about 30 seconds a side.