Preheat oven to 325°. Line a 8x8 baking pan with parchment paper, overlapping each side - this makes it much easier to pull out to cool and cut. Set aside.
Place butter, cocoa and sugar in a microwave-safe bowl and microwave for about 1 minute and 30 seconds, or until butter is melted. Mix everything together until smooth. Batter will be very gritty but will smooth out once eggs are added. Add in eggs and vanilla and mix until smooth. Pour in the salt and flour and mix until just combined. Then, mix some more until smooth and somewhat glossy. The batter will be very thick.
Pour half of the batter into your prepared baking pan and smooth it out until level. Dollop some dulce de leche on top of the batter and swirl gently with a knife. Spread the remaining brownie batter on top, making sure it is even and level. Dollop some more dulce on top (I like to make three vertical lines and swirl with my knife in 3 horizontal lines going over the vertical.) and swirl with a knife gently.
Bake for 30-40 minutes or until a toothpick comes out slightly moist with a little bit of batter left on it - underbaking is what makes them fudgy. Let them cool completely in the pan then set them in the fridge, covered, for 1-2 hours until they are set. Let them come to room temperature or you can serve them cold if you'd like.
Brownies will keep for up to 7 days in an airtight container.