Preheat the oven to 400°F:
Line a 10x15-inch jelly roll pan with nonstick aluminum foil (preferred) or regular heavy-duty foil, making sure that the foil completely covers the bottom and sides of the pan. If using regular foil, spray lightly with baking spray. Place the saltine crackers in a single layer on the bottom. 3 to 5 minutes, until the mixture comes to a boil and in color and sugar melts and emulsifies with the butter into a smooth sauce. Do not allow the mixture to boil longer than 30 seconds. Remove from heat and stir in the vanilla extract.
(Note: You're not actually making true caramel here, so you don't need to be as precise or worry about the temperature of the caramel. Just make sure it comes to a boil throughout and not just the edges and wait for it to darken slightly, then continue.) Pour the hot brown sugar mixture over the saltine crackers:
Spread to evenly coat the crackers. Move the pan to the oven:
Bake for 5 minutes. The caramel will be hot and bubbly throughout. Melt the chocolate:
Place the chocolate in a microwave-safe bowl. Cook it in the microwave in 30-second intervals at full power, stirring each time, until the chocolate has fully melted (about 1 1/2 minutes total). Pour the chocolate over the baked crackers:
Once the crackers are done baking, remove from the oven and allow to cool for 1 minute exactly, until the caramel is no longer bubbling and the crackers settle back into place. Then pour the melted chocolate over the crackers. Use a spatula to spread the chocolate evenly over the top.
