Preheat oven to 350F. Line two baking sheets with parchment paper and set aside.
In a large bowl, beat butter and sugar until completely creamy. Beat in peanut butter, egg, and vanilla until smooth. Gradually beat in flour, baking soda, cornstarch, and salt until a soft dough forms.
Roll dough into 1-in balls and place 1-in apart on prepared baking sheets. Use your thumb to indent the center of each ball. Bake cookies at 350F 9-10 minutes until edges are slightly browned. Cool cookies on pan 10 minutes then transfer to a wire cooling rack. Fill cookie centers with melted chocolate and set aside.
Make the caramel: In a medium saucepan over medium heat, melt butter. Whisk in sugar and agave and bring caramel to a boil until a deep golden brown. Remove from heat and whisk in salt and cream.
Immediately drizzle caramel over cookies and let cookies stand 10 minutes before serving. Enjoy!