Preheat oven to 350F/177C. Line a 12x17-inch (30x43-cm) jelly roll pan with parchment paper and spray sides with baking spray; set aside.
Prepare the pumpkin cake. Place the eggs, sugar and vanilla into a mixer bowl. Whisk on high speed until egg mixture is voluminous and white in color. Meanwhile, in a separate bowl, combine all the dry ingredients: flour, baking powder, cinnamon and nutmeg. Sift the dry ingredients into the egg mixture, folding gently but thoroughly after each addition. Fold in the pumpkin puree last.
Spread the cake batter evenly to the edges of prepared baking pan. Bake in preheated oven for 18 to 20 minutes, or until top is golden and set. Immediately after removing cake from oven, sprinkle the top lightly with confectioner's sugar. Place a clean kitchen towel over the top, invert the pan, and keep the parchment paper attached. Gently roll the cake along with the towel into a log; set aside to cool completely.
For Cheesecake Filling:
Prepare the cream cheese filling. First, whisk together the softened cream cheese and butter until light and fluffy. Next, add in the remaining ingredients: cold heavy cream, sweetened condensed milk, vanilla and salt. Whisk on medium speed until a fluffy frosting forms; mix carefully and do not over mix!
Assembling the Swiss Roll Cake:
Unroll cooled cake and remove parchment paper. Spread most of the filling over the cake, reserving some for frosting the outside. Spread the filling evenly to the edges, then gently roll the cake back up the same way. Transfer onto a platter and frost the top and sides.
Refrigerate the cake 4 to 6 hours or overnight, allowing the filling to set. Garnish top with cinnamon and caramel sauce before serving.