Melt salted butter in a saucepan over medium heat, stirring constantly until golden brown. Remove from heat and allow it to cool slightly.

In a large mixing bowl, combine the cooled browned butter with brown sugar until creamy. Add the egg and vanilla extract, then gradually mix in baking powder, baking soda, salt, cinnamon, flour, and graham cracker crumbs until well combined.

Using a cookie scoop, portion out dough and roll into balls. Place on lined baking sheets and slightly flatten each ball.

Preheat the oven to 350°F (175°C). Bake for 10-12 minutes until edges are golden brown. Allow cooling on sheets for a few minutes before transferring to a wire rack.

Beat together softened cream cheese and salted butter until smooth. Gradually mix in vanilla and powdered sugar until creamy.

Once the cookies are completely cooled, frost each with the cream cheese buttercream. Drizzle with caramel sauce and sprinkle with flaked salt.