Preheat the oven to 180 degrees C. Grease an 20cm square pan.
Melt the butter in a small saucepan over medium heat. Remove from the heat and stir in the unsweetened chocolate. Set aside.
In a medium bowl, beat the eggs and sugar with an electric mixer for about 5 minutes. Reduce the speed to low and pour in the chocolate and butter then stir in the vanilla. In a separate bowl stir together the matzo meal, potato flour and salt. Use a spoon to stir into the chocolate mixture until well blended. Mix in the walnuts or chocolate chips if using. Pour into the prepared pan and spread evenly.
Bake for 25 minutes in the preheated oven until the brownies are dry on top and begin to pull away from the sides.