Preheat oven to 350℉. In a medium bowl, whisk together flour, baking soda, baking powder, salt, cinnamon, ginger, nutmeg, and allspice; set aside. In a large bowl, whisk together the brown sugar, granulated sugar, butter, and eggs. Add the dry ingredients and whisk until smooth. Whisk in pumpkin purée.
Divide batter evenly among liners, filling each about halfway. Bake until tops spring back when touched, and a cake tester inserted in the center comes out clean, 20 to 25 minutes, rotating pans once if needed. Transfer to a wire rack; let cool.
Frosting
Put the chocolate in a heatproof bowl. In a small saucepan over medium-high heat, bring the cream and salt just to a boil. Immediately pour over the chocolate. Using a whisk, stir until the chocolate melts and the mixture is smooth. Let cool to room temperature and frost cupcakes.