Matzoh brei is not much more than scrambled eggs with broken up pieces of matzoh, and it's one the simplest and most delicious ways to use up leftover matzoh ever.
Melt the butter in a large skillet over medium heat. Add the onions, season with salt and pepper, and sauté for about 4 minutes, until softened.
Meanwhile, break the matzohs into pieces about 1 inch in size and place them in a bowl. Have a strainer ready. Fill the bowl with hot water so that the matzoh is covered. Let sit for 30 seconds, then drain the matzoh in a strainer.
Beat the eggs in the same bowl and season with salt and pepper. Add the matzoh and stir to combine. Transfer the egg and matzoh mixture to the pan with the onions and cook, stirring occasionally, until the eggs are as firmly cooked as you like them, breaking up the mixture (or let it cook until the bottom is firm and browned and use a spatula to flip the mixture as a single entity, then allow the scone side to brown). Transfer to a plate and serve hot.
Notes
In other savory versions of matzo brei, you might find things like cabbage or sauerkraut and mushrooms, and possibly sour cream to serve. You can make a sweet version of matzoh brei by adding other ingredients like apples, honey, and cinnamon and maybe serving it with maple syrup.