Prior to starting the cookies, you'll want to freeze 1 tbsp. balls of the dulce de leche for stuffing into the cookies. I used a 1 tbsp. cookie scoop and scooped 8 balls of dulce de leche on to a parchment lined sheet, then stuck it in the freezer. It will take ~30-60 min. to freeze, so I'd recommend doing this the night before to make things easier.
Add the butter and brown sugar to a medium sized mixing bowl. Use a hand or stand mixer to beat the mixture together until it's light and fluffy (~2-3 min.)
Add in the egg and vanilla, and beat until well combined (1 min.)
Add in the flour, baking powder, cinnamon and salt. Use a rubber spatula to fold the ingredients together just until no flour streaks remain.
Cover the bowl then place in the fridge to chill for 15 minutes, to firm up.
Scoop out 3 tbsp. scoops of the cookie dough. Use your palm to flatten the cookie dough ball down, then place a frozen ball of dulce de leche in the center of the flattened cookie.
Fold the overhanging cookie dough on top of the dulce de leche, making sure it is completely trapped inside each cookie.
Place the cookie dough balls back into the fridge for 30 minutes.*
Once the cookies have chilled, preheat the oven to 350°F / 175°C. Line a cookie sheet with parchment paper or with a silicone baking mat.
Evenly space out the cookies on the cookie sheet, leaving room for spreading.
Bake for 10-12 minutes, until the sides of the cookies just start to turn golden brown, and the top of the cookies looks just slightly wet.
If the cookies are a little misshapen, place a bowl that is slightly larger than the cookies over them, and swirl the bowl around to make the cookie more round. Let the cookies rest on the hot baking sheet for at least 5 minutes before transferring them to a wire rack to cool.
Allow the cookies to come to room temperature before frosting them.