Line a 12- by 15-inch baking sheet with cooking parchment; butter parchment. Chop 2 pounds bittersweet chocolate and place with 1 tablespoon solid vegetable shortening in a heatproof bowl that will nest in a 3- to 4-quart pan. Heat 1 inch of water in the pan just until steaming. Remove from heat and place bowl over water (bowl shouldn't touch water). Stir occasionally just until mixture is melted and smooth. Remove bowl from over pan.
Meanwhile, place 2 pounds peppermint candy in a heavy zip-lock plastic bag; pound with a mallet or rolling pin to crush. Transfer 1 1/4 cups crushed peppermint to a fine strainer; hold over melted chocolate and knock side to sift fine dust into chocolate. Reserve candy in strainer.
Stir remaining unsifted peppermint into chocolate mixture. Using a flexible spatula, scrape onto parchment and spread 1/4 to 1/2 inch thick (mixture should almost cover sheet). Sprinkle with reserved peppermint from strainer; gently press into chocolate.
Let stand at cool room temperature until completely firm, 4 to 6 hours, or overnight. Break or cut bark into pieces. Store airtight in a cool place up to 1 month.
Nutritional analysis per ounce.