Heat oven to 375°F. Line a 15 x 10-inch baking sheet with parchment paper. Arrange crackers in a single layer on prepared pan; set aside.
Melt butter with brown sugar in a large saucepan over medium-high heat; cook and stir frequently until mixture begins to boil. Boil for 3 minutes, stirring constantly. Remove from the heat. Gradually pour butter mixture evenly over crackers.
Bake for 5 minutes. Sprinkle with parmesan and chocolate chips. Return to oven for 1 minute. Spread softened chocolate chips over top. Sprinkle with toffee bits. Cool.
Refrigerate for at least 2 hours, or freezer for 30 minutes to set. Break into pieces. Store in an airtight container in the refrigerator.