Place the butter in a small saucepan over a medium heat allowing it to melt. Once melted, brown the butter gently by cooking it for further 3 minutes, stirring constantly. Pour browned, melted butter into a heatproof bowl and set aside to cool slightly for about 10 minutes.
Add soft light brown sugar into melted butter and stir to combine. Add 2 eggs and vanilla and mix well until you have smooth, glossy texture.
In a medium bowl, combine together the flour, baking soda, baking powder and salt. Add dry ingredients into the bowl with sugar and eggs mixture and stir until just combined. Cover the dough with clingfilm and place in the fridge for at least an hour.
Preheat the oven to 190 C (170C fan) and line 2 baking trays with baking parchment.
Scoop roughly about 1 tablespoon of cookie dough and form a little ball with it. Place on a baking tray, about 5 cm apart. Using a back of the spoon (or your finger) make small indents/ wells in top of the dough balls. Fill each cookie with about ½ teaspoon of dulce de leche.
Shape another cookie dough ball, and make a small indentation in it, just like in the step above. Cover the dulce de leche filled cookies with it and gently seal the edges. Gently press the top of each cookie with the palm of your hand to flatten it. Repeat until you have used up all of the cookie dough. If the cookie dough have become really soft during shaping the cookies, place them in the fridge for an extra 30 minutes before baking them.
Bake in the oven for about 10 minutes, turning them half way through, to ensure an even bake. They should be barely set in the middle but have golden edges. Allow them to cool for 5 minutes than transfer to a wire rack to cool completely. Sprinkle each cookie with sea salt flakes (optional). Enjoy!
The amount of cookies you will get may vary, depending on the size.
Try to work in batches, and keep the cookie dough as chilled as possible. Once the cookies have been shaped, you can place them in the fridge for further 30 minutes. This will allow the butter to solidify more, which will prevent cookies from spreading too much while they bake.
Store any leftover cookies in the air tight container for up to 2 days.
Freezing: You can freeze shaped, unbaked cookies for up to three months. Place the cookies on the baking tray, and into the freezer overnight. Next day, transfer frozen cookies into freezer-friendly container or a bag. If baking from frozen, add 2-3 minutes to the baking time.