Preheat oven to 450 degrees. Generously butter six 6-ounce ramekins (make sure to cover the inside of the ramekin well, but evenly. Too much butter will leave a hole in your cake). Place ramekins on a baking sheet.
In a medium bowl, melt 1/2 cup butter. Quickly add the chocolate and stir until smooth. You may need to reheat mixture for a second, be careful not to burn your chocolate. Start with 30 seconds, then stir again. Repeat until smooth. Add in flour and stir to incorporate all the flour. Set aside.
In a mixer bowl, beat eggs, egg yolks, brown sugar, vanilla, and salt. Mix on high until thick and light yellow in color. This process should take about 5 minutes in the mixer.
Add the melted chocolate/flour mixture to the egg mixture and fold with a rubber spatula until combined. Scrape the bottom and sides as you fold.
Pour the batter evenly into the prepared ramekins and bake for 8 minutes. Once the cakes are set and puffed over the edges of the ramekins, remove them from the oven and let the cakes cool in the ramekins for 1-2 minutes. Holding the hot ramekins with a dish towel, carefully invert the cakes onto dessert plates.
The molten lava cakes should pop right out, but you can run a thin-bladed knife around the edges if they are a little stuck. If desired, garnish each cake with sifted powdered sugar.