Position a rack in the center of the oven and preheat the oven to 350 degrees F. Line 2 baking sheets with parchment paper or silicone liners.
For the cookies: In a food processor, pulse together the flours, cocoa powder, baking powder, cinnamon, salt, nutmeg and the lemon and orange zests. Add the olive oil and butter and pulse until blended.
In a large bowl, whisk together the sugar, milk, rum and egg until smooth. Gradually stir the flour mixture into the egg mixture until a stiff dough forms. With damp fingers, shape the dough into 1-inch balls and place about 1-inch apart on the prepared baking sheets. Bake until the cookies are firm to the touch, 10 to 11 minutes. Cool for 10 minutes, then transfer the cookies to wire racks to cool completely, about 15 more minutes.
For the icing: Put the chocolate chips and cream in a heatproof medium bowl and place the bowl over a pan of barely simmering water. Stir frequently until the chocolate has melted and the mixture is smooth.
Dip the cookies halfway into the icing, then return them to the racks and let set at room temperature until firm, 1 1/2 to 2 hours.