Position a rack in the lower third of the oven and preheat oven to 325F. Line an 8-by-8-inch baking pan with aluminum foil leaving overhang on the sides, spray with cooking spray; set pan aside.

In a large microwave-safe bowl, combine butter, sugar, cocoa, salt, and heat on high power to melt, about 45 seconds. Stop to stir, and heat in 10-second bursts until mixture has melted and can be stirred smooth (mine took 45 seconds + 15 seconds). Batter will be very granular.

Add the vanilla, eggs, and stir vigorously until batter is thick, shiny, and well blended. Add the flour and stir until you cannot see it any longer, then beat vigorously for 40 strokes with a wooden spoon or a rubber spatula. Pour half the batter into the prepared pan and spread evenly.

Dollop half of the dulce de leche in 1 teaspoon sized balls all over the batter. Spread the remaining batter carefully over the dulce de leche. Repeat with the remaining dulce de leche on top of the brownie batter. With a knife, carefully swirl the dulce de leche slightly into the batter. Don't swirl too much - you still want to have dulce de leche pockets. Sprinkle the top with coarse sea salt, I used about 1 teaspoon.

Bake until a toothpick in the center emerges slightly moist with batter, about 22-25 minutes. Check with a toothpick - your batch may need a few minutes longer. Do not bake over 30 minutes or brownies will be prone to scorching, burning, turning dry, or setting up too hard. Brownies will firm up as they cool.

Cool brownies completely before cutting into 16 equal squares with a very sharp knife.

Brownies will keep in an airtight container at room temperature or in the refrigerator for up to 1 week, or in the freezer for up to 3 months.