Make cake: Preheat oven to 350°F. Grease and flour a 9-inch Bundt cake pan. Set aside.
Beat eggs and sugar until blended. Beat in oil. Sift flour, baking soda, pumpkin pie spice and salt into egg mixture. Fold in dry ingredients and pumpkin puree. Pour batter into pan and bake until a skewer inserted into center comes out clean, 50 to 60 minutes. Cool in pan on a wire rack for 15 minutes, then turn out onto rack to cool completely.
Make glaze: Place chocolate and corn syrup in a heatproof bowl. In a pan, warm cream over medium heat until it simmers. Pour cream over chocolate, let stand 1 minute, then whisk until smooth. Let cool to room temperature.
Place cake on a rack over a baking sheet. Drizzle glaze over cake. Let sit until set.