Preheat your oven to 350°F and line two cookie sheets with parchment paper. In a microwave-safe bowl, melt the 1/4 cup of butter and 1/2 cup of chocolate together in 30-second intervals until fully melted. Set aside to cool.
In a separate bowl, beat the 2 eggs, 1 cup of sugar, and 1 teaspoon of vanilla extract using a hand or stand mixer with the whip attachment. Mix on high for 3-5 minutes until the mixture is light and airy. It's important not to mix this by hand, as the air incorporated by the mixer creates the crinkly, brownie-like tops.
Add the melted chocolate and butter mixture to the egg mixture and stir until fully combined. You can either use a spatula or mix on low-medium speed with your mixer.
Next, add the 1 cup of flour, 1/4 teaspoon of kosher salt, 3 tablespoons of cocoa powder, and 1/8 teaspoon of baking soda. Mix on low or by hand until fully combined. The dough will be loose and resemble brownie batter more than cookie dough.
Using a mini ice cream scoop or a small spoon, drop spoonfuls of dough onto the prepared cookie sheets, spacing them about 2 inches apart to allow for spreading.
Bake the cookies for 10 minutes. They should have crinkles on top, and the edges should look crisp. Let them cool on the baking sheet for 10 minutes before transferring to a wire rack to cool completely.