Preheat oven to 325 degrees F. Line an 8 inch square baking pan with parchment paper; set aside.
Place the butter and chopped chocolate in a medium bowl set over a small saucepan of barely simmering water over low heat. Warm the chocolate and butter, stirring constantly, until completely melted and smooth. Remove from heat.
Whisk in the sugar, then whisk in the eggs and vanilla extract. Using a rubber spatula, fold in the flour, salt and chopped walnuts.
Pour the batter into the prepared baking pan, smoothing it into an even layer.
Bake for 40 to 50 minutes, or until a toothpick inserted into the center comes out with just a few moist crumbs attached. Place the pan on a wire rack and allow to cool completely before cutting into squares.
Store leftovers in an airtight container at room temperature.