Wisk flour and cocoa together in a medium bowl. Whisk egg, vanilla, and salt together in a small bowl. Cream coconut oil and brown sugar in the bowl of an electric mixer at medium speed until light and fluffy. Add egg mixture; continue beating until well incorporated. Add flour mixture; beat over low speed to form a dark, smooth dough. Divide dough in half and wrap in plastic wrap. Refrigerate until firm, at least 30 minutes. (Can be refrigerated up to two days or double wrapped and frozen for one month.)
Heat oven to 350 degrees. Working one disc at a time, roll dough on a lightly floured work surface to ⅛-inch thick, sprinkling surface with flour as needed to keep dough from sticking. Using a 2-inch cookie cutter, cut dough into desired shapes. Place dough shapes ½-inch apart on a silpat- or parchment-lined cookie sheet
Bake until golden brown, about 10 minutes. Use a thin bladed spatula to immediately transfer cookies to a cooling rack. Cool to room temperature. Repeat rolling, cutting, and baking remaining dough, rolling scraps to create as many cookies as possible.
Meanwhile, mix confectioner's sugar, ginger and milk in a small bowl, adding droplets or more milk, if necessary to make a pourable glaze. Using the tines of a fork, drizzle glaze over cooled cookies. Let sit until glaze hardens, then serve. (Cookies can be stored in an airtight tin for several weeks.)
Notes
Makes about 4 dozen 2-inch cookies
Recipe by Three Many Cooks at https://threemanycooks.com/recipes/sweet-treats/black-and-tan-cookies/