In a large bowl, cream together peanut butter, butter, sugar, and brown sugar until light and fluffy. Beat in vanilla and egg.
In a separate bowl, whisk together flour, baking soda, and salt. Gradually add to the wet ingredients and mix until just combined.
Roll dough into 1-inch balls and place on ungreased baking sheets. Flatten slightly with a fork.
Bake for 10-12 minutes, or until edges are lightly golden.
Let cool on baking sheets for a few minutes before transferring to a wire rack to cool completely.
While cookies are cooling, prepare the salted caramel topping. In a microwave-safe bowl, combine caramels and heavy cream. Microwave in 30-second intervals, stirring in between, until smooth. Stir in sea salt.
Drizzle salted caramel over cooled cookies. Let set before serving.
Notes
Store in an airtight container at room temperature.