Preheat the oven to 325 F. Place cast iron skillet on stovetop burner.
Cut butter into 6 chunks and place in skillet with the chocolate. Cook over very low heat, stirring occasionally with a wooden spoon.TIP - Because the heat is low, it can take some time, so measure out your other ingredients while it's melting, so you aren't tempted to turn up the heat!
3/4 cup unsalted butter, 3 ounces unsweetened baking chocolate
When the chocolate and butter are completely melted, remove pan from the heat and add both sugars. Stir until everything is combined.
1 cup light brown sugar, 1/2 cup granulated sugar
Add eggs, one at a time, stirring well after each addition.
3 eggs
Add vanilla and stir well.
1 teaspoon pure vanilla extract
Add flour and salt and stir until there are no traces of flour left.
3/4 cup unbleached all purpose flour, 1/4 teaspoon salt
Use a rubber spatula around the edge of the pan to clean off the sides and get all the batter into the middle.
Place skillet in the oven and bake for 50 minutes. Insert a toothpick into the center to test for doneness. The toothpick should come out clean, with the possibility of a couple of crumbs. If it's still wet, put it back in the oven and bake at 5-minute intervals.
Allow to cool on a wire rack for about 15 minutes. If you like warm brownies with ice cream and chocolate sauce, cut a wedge now. Otherwise, cool the brownies completely before cutting them into wedges.
I used a 9 3/4" cast iron skillet so they come out nice and thick. You can easily use a bigger skillet but do note that the brownies will not be as thick (plus you'll need to adjust the time in the oven). Bake until a toothpick comes out mostly clean with a few crumbs (no wet batter!).
You can substitute with a bar of bittersweet baking chocolate if desired.