Preheat oven to 350 degrees. Line a rimmed baking sheet with parchment paper.
Arrange matzos in the baking sheet to completely cover the bottom, breaking into smaller pieces as needed.
In a small saucepan, bring the butter and dark brown sugar to a boil, whisking to combine. Boil, whisking constantly, for about 3 minutes or until the butter and dark brown sugar are caramelized.
Pour mixture over matzos and spread with a spatula to cover completely. Bake for 10 minutes.
Turn off the oven and remove the baking sheet.
Sprinkle the dark chocolate chips over the top. Place the baking sheet back in the oven for 5 minutes to soften the chips.
Remove from the oven and spread the chocolate evenly over the caramelized matzos with a spatula. Let stand at room temperature for 10 minutes.
Sprinkle sea salt flakes over the toffee and chill for 30 minutes. Remove from refrigerator and break into pieces.
The toffee can be stored in the refrigerator, in an airtight container, for up to 1 week.