In a small saucepan over medium-low heat, combine the butter and ¾ cup of the sugar.
Stir until melted and glossy, then bring to a gentle simmer. Cook for 1–2 minutes until syrupy and the sugar is mostly dissolved, about 230°F. Remove from heat and cool slightly.
In a large mixing bowl with a hand mixer, beat the eggs, egg yolk, and remaining ¾ cup sugar on medium speed until pale, thick, and creamy, about 2–3 minutes.
Mix in the vanilla bean paste.
Slowly drizzle the warm butter mixture into the egg mixture while mixing on low speed.
Mix in the melted dark chocolate until glossy and combined.
Sift in the cocoa powder, flour, espresso powder, and sea salt. Mix just until combined.
Fold in the chopped dark chocolate.