Preheat oven to 350°F (177°C). Line rimmed baking sheets with parchment paper or silicone baking mats.
Place 11.5 ounces (326 g) chocolate chips and 2 tablespoons (28 g) butter in a small saucepan over medium-low heat. Stir frequently until completely melted and smooth. Remove from heat and let cool completely, about 8–10 minutes.
In a large bowl, whisk together 1/2 cup (60 g) all-purpose flour, 1/4 teaspoon (1 g) baking powder, 1/4 teaspoon (1 g) kosher salt, and 3 tablespoons (16 g) unsweetened cocoa powder. Set aside.
Fit a stand mixer with the paddle attachment. Add 1 cup (198 g) granulated sugar and 1/4 cup (4 tablespoons, 57 g) softened butter to the mixer bowl. Beat on medium speed until light and fluffy, about 3 minutes, scraping down the bowl as needed.
With the mixer on low-medium, add the 3 eggs one at a time, allowing each egg to incorporate before adding the next. Add 2 teaspoons (9 g) vanilla extract and mix until combined.
Increase mixer speed to medium-high and beat until the mixture is pale, light, and fluffy, about 7–10 minutes. Scrape the bowl once or twice during this step.
Reduce mixer speed to low and slowly pour in the cooled melted chocolate. Mix just until evenly incorporated.
Add the dry flour-cocoa mixture and stir on low speed (or fold by hand) until just combined. Do not overmix.
Stir in 1 cup (170 g) milk chocolate chips until evenly distributed.
Drop tablespoon-sized scoops of dough onto the prepared baking sheets, spacing them about 3 inches apart.
Bake in the preheated oven for 12–15 minutes, until the edges are set (centers may still look slightly soft).
Remove the cookies from the oven and allow them to cool completely on the baking sheet before transferring, as they are fragile while warm.