Cream soft butter with sugar until smooth, stir in egg and vanilla extract. Combine flour, baking powder and salt and stir into butter-sugar mixture until a compact dough forms. Refrigerate dough for 30 minutes.
Preheat oven to 180 degrees top/bottom heat (convection oven: 160 degrees). Line a baking tray (30 cm x 40 cm) with baking paper. Cut the caramel candies into small pieces.
Form the dough into a roll and divide into 25 equal portions. Shape each portion of dough round and press into the chopped caramels. Place on baking sheet and bake in preheated oven for about 12 minutes, then let cool briefly.
Warm dulce de leche slightly to liquefy and transfer to a paper bag. Slit bottom of paper bag slightly and pass back and forth over cookies to create thin caramel stripes. Sprinkle with coarse sea salt. Caramel Cookies will keep, wrapped airtight, at room temperature for at least 10 days.