In a large bowl, whisk together the flour, cocoa powder, baking soda, and salt. Set aside.
In a large mixing bowl or bowl of the stand mixer fitted with the paddle attachment, add the butter, brown sugar, and 1/3 cup (66 g) of sugar. Beat with a hand mixer or the stand mixer until light and fluffy.
Add the milk and vanilla and beat until well combined.
Add the flour mixture to the butter mixture. Mix until just combined.
Place the remaining 3 tbsp (37 g) of sugar in a small bowl. Roll tablespoon-sized (~18 g) balls of dough in the sugar.
Using the bottom of a 1/2 teaspoon measuring spoon, press divots into the centers of each ball of dough. Freeze until solid, about 2-4 hours or overnight.
Preheat the oven to 350°F (180°C). Line two baking sheets with parchment paper. Place the prepared balls of dough on the baking sheets, leaving room in between each.
Bake for 7-9 minutes. Once you remove the cookies, press into the centers again, if needed, to help retain the shape. Allow to cool slightly.
Place the chocolate chips into a heat-safe bowl. Heat the milk in the microwave or on the stovetop until it begins to simmer. Pour over the chocolate and let set about three minutes, then whisk until very smooth and creamy.
Place a dollop of chocolate into each cookie divot then top with sprinkles. Leave at room temperature or refrigerate until set. Enjoy!