Preheat your oven to 350°F (175°C). Lightly grease a 9-inch pie pan.

In a medium saucepan over low heat, combine the unsweetened chocolate and butter. Stir constantly until both are completely melted and smooth. Remove from heat.

Whisk in the granulated sugar, all-purpose flour, and vanilla extract until well combined.

Add the eggs one at a time, whisking well after each addition until the batter is smooth and glossy.

Pour the batter into the prepared pie pan, spreading it evenly.

Bake for 27 to 30 minutes, or until the edges are set and the center is still slightly fudgy.

Let the pie cool slightly before serving warm. Serve with chocolate sauce and vanilla ice cream, if desired.