Preheat oven to 350 degrees. Make cookies: Sift together flour, cocoa powder, malted milk powder, baking soda, and salt. With an electric mixer, beat butter and sugar on medium-high speed until pale and fluffy. Mix in egg, vanilla, creme fraiche, and hot water. Reduce speed to low; mix in flour mixture.
Space tablespoon-size balls of dough 3 1/2 inches apart on parchment paper-lined baking sheets. Bake until flat and just firm, 10 to 12 minutes. Let cool on parchment on wire racks.
Making filling: Melt chocolate and butter in a heatproof bowl set over a pan of simmering water, stirring. Let cool. With an electric mixer, beat malted milk powder and cream cheese on medium speed until smooth. Gradually mix in half-and-half, chocolate mixture, and vanilla. Refrigerate, covered, until thick, about 30 minutes. Mix on high speed until fluffy, about 3 minutes.
Assemble cookies: Spread a heaping tablespoon filling on the bottom of one cookie. Sandwich with another cookie. Repeat.
Cookies can be refrigerated between layers of parchment in airtight containers up to 3 days.