Position a rack in the middle of the oven and preheat to 350. Line a standard 12-cup muffin pan with paper or foil liners. (I always make 13 cupcakes, sometimes 14 with this recipe. 12 gives me muffin tops, which is not pretty).
Sift together the flour, cocoa powder, baking soda, and salt into a bowl. (Alternately use a whisk and mix them together in a bowl).
In another bowl, with an electric mixer on medium-high speed, beat the granulated sugar, brown sugar, and butter together until light and fluffy, 2-3 minutes. Add the egg and vanilla and beat until combined. Add the flour mixture in 3 additions, alternating with the water and buttermilk, beating on low speed until just combined; scrape down the sides of the bowl as needed (not necessary if you're using your beater blade). Beat on medium-high speed just until no traces of flour remain, about 30 seconds; do not overbeat.
Divide the batter evenly among the prepared muffin cups, filling each about three-fourths full (or use this scoop, scantly filled). Bake until a toothpick inserted into the center of a cupcake comes out clean, 18-20 minutes. Let the cupcakes cool in the pan on a wire rack for 5 minutes. Transfer the cupcakes to the wire rack and let cool completely, about 1 hour.
Combine cream and chocolate in a microwave-safe bowl and microwave at 50% power, stirring often, until melted, 2 to 4 minutes. Stir in vanilla and salt. Let cool to barely warm.
Hollow out the center of each cupcake. You can do this with a knife, but this cupcake corer tool is worth the nearly $6... you'll be done in just a few minutes. I often delegate this out to my kids (after insisting they wash their hands at least twice).
Once the filling is cool to touch and thickened, fill the cupcake holes with the chocolate filling. It may settle, so don't be surprised if you have to do a second round to top off the holes.
Using a stand mixer fitted with the beater blade (or paddle), beat butter, cream, vanilla, salt, and vanilla bean, if using, on medium-high speed until smooth, about 1 minute. Reduce speed to medium-low, slowly adding sugar, and beat until incorporated and smooth, about 4 minutes.
Increase speed to medium-high and beat until frosting is light and fluffy, about 5 minutes.
Spoon the crushed candy canes on top immediately after frosting.
Frosted cupcakes will keep in the refrigerator for up to 3 days. Bring them to room temperature before serving, about 2 hours.
Source: Cake from "Cupcakes" cookbook by Shelly Kaldunski, Chocolate Filling and Vanilla Buttercream from America's Test Kitchen