Preheat oven to 350 degrees F. Prepare a 9 X 13-inch baking dish by lining it with tin foil and generously coating it with cooking spray.
Put the saltine crackers in the bottom of the prepared baking dish, making sure they are in a single layer.
Place butter and the brown sugar in a small saucepan. Stir constantly as you bring the mixture to a boil.
Upon reaching a boil, lower the heat and allow to simmer for 3-5 minutes, uncovered until mixture has slightly thickened.
Stir mixture frequently to prevent it from burning or scorching. When the mixture has thickened, remove it from heat and wait for 30 seconds before stirring in the vanilla extract.
Pour mixture over the saltines and spread so that they are completely covered.
Bake for 5-7 minutes, or until brown sugar mixture begins to bubble. Upon removing from the oven, allow to sit for 3-5 minutes before sprinkling peanut butter chips over the toffee mixture.
Let the chips sit for 3-5 minutes so that they may soften. Spread to cover toffee mixture and allow to cool completely and harden before breaking apart to serve.