Melt bittersweet chocolate in a bowl set over a saucepan of simmering water, stirring until smooth; remove from heat. Whisk together flour, cocoa powder, spices, baking soda, baking powder, and salt. Beat together butter and brown sugar in a bowl with an electric mixer on medium-high speed until creamy, about 3 minutes. Add egg and molasses and beat until smooth. Beat in bittersweet chocolate, then flour mixture, until combined. Divide dough in half; form each half into a rectangle and wrap in plastic wrap. Refrigerate until firm but still pliable, about 30 minutes. Dough can be made 3 days ahead and stored in refrigerator, or frozen up to 1 month.
Preheat oven to 350 degrees. Roll out each piece of dough to a rectangle 1/8-inch thick, with 1 side roughly 12 inches long, on a lightly floured piece of parchment. Transfer rectangles on parchment to baking sheets and refrigerate until firm, 30 minutes. Using a pizza cutter or sharp knife, cut into 1/4-to-1/2-inch-wide irregular strips, each about 12 inches long. Separate strips on parchment-lined baking sheets and freeze until firm, about 30 minutes. Bake until slightly darker around edges, about 12 minutes. Let twigs cool completely on baking sheets.
Melt white chocolate in a bowl set over a saucepan of simmering water, stirring until smooth. Paint chocolate along length of each twig with a pastry brush to create a faux-bois look. Refrigerate until chocolate sets, about 15 minutes. Twigs can be made 3 days ahead and stored in a cool place.