Preheat your oven to 375 degrees. Brew 1 1/2 cups of coffee. While the coffee is brewing, butter (or spray with cooking spray) the bundt pan and then dust with cocoa powder. Do this well to ensure the mini bundt cakes come out of the bundt pan.
In a microwave safe bowl, melt the butter for 20 seconds. Mix with the coffee and cocoa powder. Stir with a wire whisk. Once everything is combined, add the sugar and whisk until it has dissolved. Transfer the mixture to a large bowl and set aside to cool for about 5 minutes.
In another bowl, combine the flour, baking soda, and salt. Mix. In a separate bowl, whisk the eggs and vanilla.
Whisk the eggs into the chocolate mixture. Slowly add the flour mixture and continue to whisk. Once all of the ingredients have been combined you will be left with a batter with the consistency of a slightly thick soup.
Pour the batter into the mini wells of the bundt pan and bake for about 20-25 minutes or until a toothpick inserted comes out clean.
Remove the bundt pan from the oven and let cool for at least 20 to 30 minutes. Once cooled, gently run a butter knife or fork around the sides of each cake to gently remove from the bundt pan. You can also loosen the edges of each mini bundt cake with a butter knife or fork and place a wire rack directly up against your bundt pan and invert so the mini bundt cakes just fall out.