Preheat the oven to 350 °F. Generously butter a 9"x3" spring-form pan. Set aside 1 oz (¼ cup) of the hazelnut flour. Use half of the set-aside hazelnut flour to dust the buttered pan.
Melt 4 oz unsalted butter in a small saucepan. Cook until the milk solids sink to the bottom of the pan and become brown. Drain the butter into a microwave safe bowl, leaving the solids in the pan.
Add the chopped 6 oz semi-sweet chocolate into the bowl with the browned butter. Microwave for 30 seconds and then stir. Continue microwaving and stirring in 30 second increments until all the chocolate is melted.
Stir the remaining 5 oz of hazelnut flour and 2 oz (¼ cup) of the granulated sugar into the chocolate mixture. Add 2 teaspoon vanilla extract.
In a large mixing bowl, whisk 6 large eggs, ¼ teaspoon table salt and remaining 4 oz (½ cup) sugar on medium-high speed until tripled in volume and the color turns pale yellow. Fold ⅓ of the eggs into the chocolate then fold the chocolate into the remaining eggs. Mix until no streaks of eggs are visible.
Pour the batter into the prepared pan. Sprinkle the rest of the set-aside hazelnut flour evenly across the top of the batter.
Bake until the batter is set and a toothpick inserted in the center comes out with a few wet crumbs, about 30-35 minutes.
Cool 10 minutes before unmolding. Serve the cake slightly warm or room temperature.
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