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 3 baking trays with baking parchment.
Scoop roughly about 1 tsp 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 in top of the dough balls. Fill each cookie with about 1/2 tsp 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. Repeat until you have used up all of the cookie dough.
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.
The amount of cookies you will get may vary, depending on the size.To ensure flatter cookies, with a bit of that crinkled texture, use the 'pan banging' method. After cookies baked for about 4-5 minutes, take the baking tray out of the oven and whack it against the hard surface, then return to the oven. This will create that 'wrinkled' texture and appearance.