In a food processor fitted with an S-shaped blade (the standard blade), combine all the flour, baking soda, cocoa powder, sugar, butter, eggs, sour cream, vanilla extract, and peppermint extract. Place the lid on and pulse ingredients a few times to combine, then process for a few seconds until you have a thick, smooth batter.
Measure out ½ cup of boiling water, hit the “ON” button on the food processor, and stream the boiling water into the chocolate batter using the spout on the lid. Blend mixture until smooth and very liquid-y.
Remove lid and carefully scrape down the sides of the bowl to dislodge any thick pieces of batter into the liquid. Replace lid and pulse batter a few more times to make sure all ingredients are thoroughly combined.
Remove bowl from processor stand, remove lid, and fold the floured mint chips and chocolate chips into the batter. The batter will be chunky but liquid-y at this stage.
Slowly pour the batter into the prepared Bundt pan. Bang the filled pan firmly on the countertop to release any air bubbles, then place pan on the baking sheet and place in the oven.
Bake cake at 325F for 45 minutes, or until a toothpick inserted in the middle of the cake (away from the center tube) comes out clean.
Place Bundt pan on a wire rack. Let cake cool completely before removing it from the pan.