Preheat the oven to 350 degrees F. Generously grease a 10- to 12-cup bundt pan with the butter, then dust it with flour, tapping out any excess.
Whisk together the flour, sugar, baking soda and salt in a large mixing bowl; set aside.
Heat the coffee, coconut oil, cocoa powder, semisweet chocolate and 1/3 cup of the coconut milk in a small saucepan over medium heat, stirring frequently, until the chocolate is melted and makes a smooth sauce, 4 to 5 minutes. Fold the chocolate mixture into the flour mixture until smooth and combined. Fold in the vanilla and eggs until smooth.
Pour the batter into the prepared pan and bake until a toothpick inserted in the center comes out clean, 45 to 55 minutes. Let the cake cool in the pan for 10 minutes, then turn it out onto a cooling rack set inside a baking sheet to cool completely, 1 to 2 hours.
Meanwhile, make the ganache: Put the white chocolate in a heatsafe bowl; set aside.
Sift the matcha into a saucepan and whisk in 1/4 cup of the coconut milk. Keep whisking until no lumps remain. Whisk in the remaining coconut milk. Set over medium heat and cook, stirring often, until the mixture just begins to boil. Pour it over the white chocolate, let it sit for a few seconds, then stir it all together until the chocolate melts. Let the ganache cool slightly, stirring often, until no longer hot to the touch and thickened but still pourable.
Pour 1 cup of the ganache over the cake and refrigerate until hardened, about 10 minutes. Pour the remaining ganache over the cake and refrigerate until hardened, about 10 minutes. Scrape the ganache at the bottom of the baking sheet back into the bowl and pour it over top once more. Let it harden, about 10 minutes.
Decorate the cake with candy eyeballs, then slice and serve.