Heat the oven to 350° with the rack in the middle. Brush the soft butter generously all over the inside of a 12-cup Bundt pan, then dust lightly with cocoa powder, shaking off any excess.
In a large mixing bowl, whisk together the eggs, oil, licorice root powder, and hot water. Add the sugar and whisk well to combine. Sift together the cocoa powder, flour, baking soda, baking powder, and salt in a bowl.
In three additions, add the dry ingredients to the wet ingredients, stirring between each addition until incorporated before adding the next. Fold in the sour cream, chocolate, and licorice chews.
Pour the batter into the prepared pan and bake until a wooden pick inserted into the center comes out clean, 50–60 minutes. Transfer to a wire rack and let the cake cool in the pan for 10 minutes. Invert the cake onto the rack; remove the pan and let cool completely. Dust with cocoa powder just before serving. Cake can be stored at room temperature, wrapped tightly in plastic, for up to 3 days.