Preheat oven to 250°. Line a cookie sheet with foil and arrange as much matzah as will fit on the sheet (about 4 pieces of matzah).
Melt butter in a medium-sized saucepan over medium heat. Once melted, add brown sugar and stir to combine,
Cook until the butter bubbles and the sugar has melted.
Remove the pan from heat and stir in the vanilla extract.
Pour the toffee mixture over the matzah and spread it until it completely coats the matzah.
Bake the toffee-coated matzah, 25-30 minutes.
Remove the baking sheet from the oven and cover the matzah with chocolate chips. Put the cookie sheet back into the oven and bake until the chocolate begins to melt about 3-4 minutes.
Remove the sheet and spread the melted chocolate over the top of the matzah.
Sprinkle a generous amount of flaked sea salt over the top of the chocolate and place the baking sheet into the refrigerator for 2 hours, or until the chocolate and toffee is set.
Remove the baking sheet from the refrigerator and break the matzah into pieces before serving.