Heat the 3 tablespoons of butter in a nonstick sauté pan and gently cook the onions until soft and caramelized. Let them cook on medium-low heat for 3 minutes, and then sprinkle a little of the salt and ⅛ teaspoon sugar (if desired) over them. Cover the pan and turn the heat down to low. Cook, stirring occasionally, for 15 to 20 minutes. Remove the onions from the pan and set aside. Wipe out the pan with a paper towel.
Beat the eggs with the remaining salt and the black pepper in a large bowl. Break the matzo into small pieces by hand, place the pieces in a bowl, and cover them with hot water to soften them. Let them stand for a minute and then strain them through a fine-mesh colander.
Combine the beaten eggs with the caramelized onions and the softened matzo pieces. Cook using one of the following options:
Melt 2 tablespoons of unsalted butter in a sauté pan over medium-high heat. Let the butter heat up for a minute and then pour in the matzo-egg mixture. Cook over medium heat, moving the mixture around constantly, until the eggs are just barely set—you want them to be a little bit runny. This should take 3 to 4 minutes or so. Serve immediately.
Option Two (my preferred option):
Melt 1 tablespoon of unsalted butter in each of two 8-inch nonstick skillets over medium-low heat. Let the butter heat up for a minute and then evenly divide the matzo-egg mixture between the two pans. Cook the mixture over medium-low heat for 2½ minutes without touching it (almost as if you were making a pancake), then flip over and cook for 2½ more minutes. Slide each onto a plate.
Top each serving of Matzo Brei with a tablespoon of sour cream, a tablespoon of applesauce and chopped chives to taste.
3 tablespoons butter
1 small white onion, finely chopped
¼ teaspoon salt, divided
¼ teaspoon black pepper
4 sheets of matzo
2 tablespoons unsalted butter
2 tablespoons sour cream, for topping
2 tablespoons applesauce, for topping
Chopped chives to taste