Melt the Chocolate and Butter : In a microwave-safe bowl, combine the butter and semi-sweet chocolate. Microwave in 20-second intervals, stirring after each, until the mixture is fully melted and smooth. Set aside to cool slightly.
Mix the Wet Ingredients : In a large bowl, whisk the eggs and granulated sugar together until light and fluffy, about 1-2 minutes. Add the vanilla extract and the melted chocolate mixture, stirring until well combined.
Combine the Dry Ingredients : In a separate bowl, whisk together the all-purpose flour, cocoa powder, baking soda, and salt. Gradually fold the dry ingredients into the wet ingredients, mixing just until combined.
Shape the Cookies : Preheat your oven to 350°F (175°C) and line a baking sheet with parchment paper. Using a tablespoon or small cookie scoop, drop dollops of the dough onto the prepared baking sheet, spacing them about 2 inches apart.
Bake the Cookies : Bake for 8-10 minutes, or until the edges are set but the centers are slightly underbaked. The cookies will continue to set as they cool. Let the cookies cool on the baking sheet for 5 minutes, then transfer them to a wire rack to cool completely.