Preheat oven to 350°F. Line 2 baking sheets with parchment paper or silicone mats.
In a large bowl, sift together flour, malted milk powder, cocoa, baking powder, and salt; set aside.
In the bowl of a stand mixer fitted with the paddle attachment, beat the butter and sugar together on medium speed for about 3 minutes, until thoroughly combined. Add the eggs one at a time, beating for 1 minute after each addition. Beat in the vanilla until combined. Add half of the dry ingredients and beat at low speed just until combined. Mix in the milk, then the remaining dry ingredients, mixing until just combined. With the mixer on low, mix in the malted milk balls and chopped chocolate.
Drop the dough by rounded tablespoonfuls on to the sheets, leaving about 2 inches of space between each. Bake for 11 to 13 minutes, rotating the baking sheets front to back and top to bottom halfway through the baking time. Let the cookies rest for 2 minutes before using a wide metal spatula to transfer them to the racks to cool to room temperature.