Preheat oven to 350°F and coat a 12-cup bundt pan with nonstick spray.
Whisk together boiling water and cocoa, then set aside to cool.
Whisk together flour, baking soda, baking powder, and salt in a medium bowl.
Beat butter, sugar, and peppermint extract in a large mixer bowl at medium speed until well blended (about 3 minutes); add eggs one at a time and beat well.
Whisk yogurt into cooled cocoa mixture.
Add half of flour mixture to sugar mixture and beat until just combined.
Add cocoa mixture, then finish with remaining flour mixture.
Fold in chocolate chips.
Spoon batter into prepared pan and smooth with an offset spatula; tap pan sharply to remove air bubbles.
Bake 34 to 35 minutes, until cake begins to pull away from edges of pan and a toothpick inserted in the center comes out clean.
Cool in pan on a wire rack for 10 minutes; carefully invert onto rack and cool completely.
For the glaze, combine powdered sugar, milk, butter, and peppermint extract in a small bowl. Place wire rack with cooled cake over a piece of wax paper; drizzle cake with glaze and sprinkle with crushed candy canes; let set before serving.
Store leftovers in an airtight container at room temperature.