To make the cookies: Add all of the ingredients to a medium-size bowl and mix until it forms a pliable dough. Add more milk if the dough needs to come together more.
Preheat the oven to 180°C (350°F).
Place the dough on a lightly floured surface. Flatten the dough with a rolling pin so it is about 8mm (0.3 inch) thick. Use a gingerbread cookie cutter to cut shapes out of the dough. Carefully place each cookie on a lined baking tray with a little space in between each cookie. You may need to use a butter knife or spatula to transfer them,
Collect the excess dough, press it together and roll it out again. Repeat until you have no more dough.
Bake the cookies in the oven for 5-10 minutes (depending on the size of your cookies). The edges of the cookies should be slightly golden brown. Allow the cookies to completely cool on the baking tray.
To make the frosting, combine all ingredients and mix until it forms a thick paste. Add more coconut butter to thicken and more milk to thin the frosting.
Use a piping bag or a sharp object to decorate the gingerbread as desired.
Enjoy immediately! Cookies are best enjoyed on the day of baking. Alternatively, store them in an airtight container for up to 1 week.