Preheat the oven to 375° Fahrenheit. Grease a cookie sheet (15x10x1 inches) and line with parchment paper. Grease the parchment paper and be sure the corners are pushed in; set aside. Separate the eggs into two medium bowls (be sure that the whites are in a clean, dry bowl). Using an electric mixer, beat the egg whites until soft peaks form. Add the white sugar and continue to beat until stiff peaks form, then set aside. Using the same mixer in the other bowl, beat the egg yolks with the brown sugar, vanilla, and pumpkin until fully combined.
In a separate, smaller bowl, whisk together the dry cake ingredients (flour, starch, baking powder and soda, salt, spices), then dump dry ingredients into the pumpkin batter and use a spatula to fully mix. Fold in the egg whites 1/3 at a time, careful not to deflate the mixture. When blended, pour the batter into the prepared pan and carefully smooth so that it evenly coats the pan. Bake for 13-15 minutes until the sponge cake is firm to the touch.
Let the cake cool for a few minutes out of the oven, then dampen a kitchen towel and lay it flat on a counter. Lift the parchment paper and cake onto the kitchen towel, and dust the cake with powdered sugar. Roll the entire thing up, towel and all, from short end to short end, and let the cake sit, rolled, until completely cool. This will form the cake into a spiral which will make it easier to roll once you fill it.
While the cake is cooling, make the filling. In a large bowl, using the electric mixer, beat together the room temperature butter, cream cheeses, powdered sugar, and vanilla until blended. Add the milk and beat until you have a slightly thinner consistency.
Once the cake is cool, carefully unroll and, using a spatula or a butter knife, spread the cream cheese filling evenly over the entire cake. Then carefully roll the cake back up in a tight spiral. The cake can be stored in the fridge before serving, but we recommend serving soon after cake is complete!