Milk-Chocolate Cookies with Malted Cream

Preheat the oven to 350 degrees F. Line 2 baking sheets with parchment paper.
MAKE THE COOKIES: In a large bowl, using an electric mixer, beat the butter with the brown sugar and granulated sugar until smooth. Add the melted chocolate and vanilla and beat until smooth. In a small bowl, whisk the flour with the cocoa powder, baking soda and salt. Add the dry ingredients to the bowl and beat at low speed just until incorporated. Roll the dough between 2 sheets of parchment paper to a scant ¼-inch thickness and refrigerate until firm, about 15 minutes.
Using a 2-inch round cookie cutter, stamp out as many rounds as possible and transfer to the baking sheets, 1 inch apart. Gather the scraps and chill, with the cut-out rounds, for 10 minutes. Reroll the scraps and stamp out more rounds.
Bake the cookies in the lower and middle thirds of the oven for about 10 minutes, until dry and set; shift the pans halfway through baking. Transfer the cookies to a rack and let cool completely.
MAKE THE FILLING: In a bowl, using an electric mixer, beat the butter with the malt powder at medium speed until light, 3 minutes. Add the vanilla and confectioners’ sugar and beat at low speed just until combined. Transfer the filling to a pastry bag fitted with a ½-inch plain tip. Arrange half of the cookies on a work surface, bottom side up, and pipe a 1-inch mound of filling onto each. Sandwich with the remaining cookies and serve.