Line a 9x9-inch baking pan with parchment paper, leaving some overhang for easy removal later.
In a heavy-bottomed saucepan, combine the butter, granulated sugar, corn syrup, and heavy cream. Stir well to combine the ingredients.
Place the saucepan over medium heat. Stir the mixture constantly until the sugar has dissolved and the butter has melted.
Once the mixture is smooth, whisk in the unsweetened cocoa powder and instant espresso powder.
Bring the mixture to a boil, then reduce the heat to medium-low. Attach your candy thermometer and continue to cook until the caramel reaches 245°F (118°C).
Once the caramel reaches the desired temperature, remove it from the heat and stir in the pure vanilla extract.
Quickly pour the caramel into the prepared baking pan, spreading it evenly.
Let the chocolate caramels cool at room temperature for several hours until fully set.
Once set, lift them out of the pan using the parchment and cut into small squares or rectangles.