Preheat oven to 400°F. Line a 13x18-inch rimmed baking sheet with aluminum foil or a silicone liner. If using foil, spray it lightly with nonstick spray.
Arrange the graham cracker sheets in a single layer on the prepared pan, side by side, breaking sheets as needed to fill the pan (about 15 sheets).
In a medium saucepan combine the 1 cup unsalted butter (cut into pieces) and 1 cup light brown sugar. Heat over medium until the butter melts, then bring the mixture to a rolling boil.
Boil the butter–sugar mixture for 3 minutes, stirring occasionally. Use caution—the mixture will be very hot.
Immediately and carefully pour the hot toffee mixture evenly over the graham crackers. Use a rubber spatula to spread the toffee into an even layer over the crackers—work quickly before it begins to set.
Place the pan in the preheated oven and bake for 4 minutes.
Remove the pan from the oven. Drop the 3/4 cup peanut butter (not natural) in small dollops across the toffee layer using a spoon.
Return the pan to the oven for 1 minute to soften the peanut butter.
Remove the pan and use an offset spatula or the back of a spoon to spread the softened peanut butter into an even layer over the toffee.
Evenly sprinkle the 2 cups semi-sweet chocolate chips over the peanut butter layer.
Return the pan to the oven for 1 minute to soften the chocolate chips. Remove and gently spread the melted chocolate with an offset spatula—spread lightly to preserve some texture.
Immediately sprinkle the 3/4 cup roasted salted peanuts (chopped) evenly over the melted chocolate.
Allow the pan to cool to room temperature on a wire rack, then transfer to the refrigerator and chill until completely firm, at least 2 hours.
Once chilled and firm, break the toffee into irregular pieces. Store the finished toffee in the refrigerator.