Preheat the oven to 450 degrees F.
Add the eggs, egg yolks, granulated sugar, table salt, and vanilla extract to the bowl of a stand mixer fitted with the paddle attachment (or a large bowl and an electric hand mixer).
Whip the egg mixture until light and fluffy (3-4 minutes) then set aside until needed.
Add the unsalted butter and chocolate to a metal bowl that will sit on top of the saucepan (this is a double boiler).
Add one inch of water to a saucepan and bring it to a simmer, then reduce the heat.
Place the bowl with the chocolate on the saucepan. Stir the chocolate and butter with a rubber spatula until it's smooth.
Pour ½ cup of the melted chocolate into the egg mixture and fold together using a rubber spatula for about 20 seconds to temper the eggs.
Pour in the remaining chocolate into the egg mixture using a rubber spatula to gently fold into the mixture.
Add the all-purpose flour to the chocolate, gently folding it into the mixture with a rubber spatula until well combined.
Butter and flour six 8-ounce ramekins.
Divide the batter evenly among the ramekins and place the ramekins on a large baking sheet leaving a few inches between each ramekin.
Place the baking sheet on the center rack of the preheated oven and bake for for 9-10 minutes.*The cakes need to bake long enough to form a crust around the chocolate filling without baking all the way through. Remove the baking sheet from the oven and let lava cakes sit for 2-3 minutes to cool slightly. Then, run a small knife around the edges to loosen the cake.
Place a plate upside down on the ramekin. Holding onto both the plate and the ramekin, carefully flip it so the cake releases onto the plate.*Tap lightly on the bottom of the ramekin if the cake doesn't release from the ramekin. Dust with powdered sugar (or cocoa powder) and serve warm with homemade whipped cream or vanilla ice cream.