In a large mixing bowl, beat the butter with an electric mixer on medium to high speed for 30 seconds. Add the granulated sugar, brown sugar, and baking soda. Beat mixture until combined, scraping sides of bowl occasionally. Beat in the eggs, vanilla, and melted chocolate until combined. Beat in as much of the flour as you can with the mixer. Stir in remaining flour and the malted milk powder. Stir in the malted milk balls.
Drop dough from a rounded teaspoon 2-1/2 inches apart on an ungreased cookie sheet. Bake in a 375 degree F oven about 10 minutes or until edges are firm. Cool on cookie sheet for 1 minute. Transfer cookies to a wire rack; cool. Makes about 36 cookies.