Make the cookies: Preheat the oven to 325 degrees F. Line 2 baking sheets with parchment paper. Combine the flour, cocoa powder, sugar, malted milk powder, baking soda and salt in a large bowl. With a mixer on medium-high speed, add the vanilla and then the butter, a few pieces at a time, and mix until the dough looks like wet sand and holds together when pinched, about 5 minutes. Scrape the dough onto a sheet of parchment paper and pat into a 1/2-inch-thick round. Cover with another sheet of parchment paper and refrigerate until the dough is slightly firm, about 10 minutes.
Roll out the dough between the parchment sheets to 1/4 inch thick. Peel off the top sheet and cut the dough into squares or rounds using 1 1/2-to-2-inch cookie cutters. Reroll the scraps and repeat. (Refrigerate the dough if it gets too soft.) Place the cookies 1 inch apart on the prepared baking sheets.
Bake until the cookies are set and no longer shiny, 8 to 10 minutes. Let cool 5 minutes on the baking sheets, then transfer to a rack to cool completely.
Prepare the filling: Combine the white chocolate, malted milk powder, salt and vanilla in a large bowl. Bring the cream to a simmer in a saucepan over medium heat, then pour over the white chocolate mixture and stir until smooth. Refrigerate until cold, about 25 minutes. Beat with a mixer until thick and spreadable, about 1 minute.
Spread about 2 teaspoons of the filling on the underside of half of the cookies, then sandwich with the remaining cookies. Dust with cocoa powder, if desired. Store in the refrigerator up to 5 days.