Place an oven rack in the center of the oven. Preheat the oven to 375 degrees F. Butter an 11-by-17-inch rimmed, nonstick baking sheet. Line the pan with parchment paper and butter the parchment paper. Lay a clean kitchen towel on a work surface and dust with powdered sugar.
For the cake: In a medium bowl, whisk together the flour, cinnamon, baking powder and salt. In another medium bowl, using an electric hand mixer on high speed, beat the sugar and eggs together until thick, about 2 minutes. Beat in the pumpkin puree. Gradually beat in the flour mixture. Pour the batter into the prepared pan and spread evenly. Bake until the cake springs back when touched, about 12 minutes.
Run a thin metal spatula around the edges of the cake and immediately invert the pan onto the kitchen towel. Carefully peel off the parchment paper. Starting at the narrow end, roll up the cake and towel together into a log. Cool completely on a wire rack, about 45 minutes.
For the filling: Place the chocolate and butter in a medium bowl. Place the bowl over a pan of barely simmering water. Stir until the chocolate is melted and the mixture is thick, about 2 minutes. Add the mascarpone cheese and, using an electric hand mixer, beat until smooth.
Carefully unroll the cake and remove the towel. Using a spatula, spread the filling over the cake. Roll up the cake and wrap in plastic wrap. Refrigerate for at least 2 hours. When ready to serve, cut the roll into 1/2-inch-thick slices and arrange on a platter.