Place a rack in the lower third of the oven and preheat to 350 degrees . Line a 12-cup muffin pan with baking liners. Using an electric mixer, beat the cream cheese and confectioners' sugar for 3 minutes. Beat in 1 egg white and 1/2 teaspoon vanilla.
In a bowl, whisk the flour, pumpkin pie spice, baking powder and 1/2 teaspoon salt. In another bowl, mix the pumpkin puree, 2 eggs, granulated sugar, oil and 1 teaspoon vanilla. Whisk in the flour mixture.
Layer each muffin cup with some of the pumpkin batter, then the cream cheese mixture, then more of the batter. Bake until springy to the touch, 25 minutes. Let cool.
Using the electric mixer, beat the brown sugar, remaining 4 egg whites and remaining 1/4 teaspoon salt. Fill a medium saucepan with enough simmering water to reach a depth of 1 inch; place the mixing bowl on top. Whisk the mixture until it registers 160 degrees on an instant-read thermometer.
Transfer the bowl back to the mixer and beat at high speed until fluffy; lower the speed and beat to room temperature, about 5 minutes. Add the butter, 1 tablespoon at a time, then beat at high speed for 5 minutes. Beat in the remaining 1/2 teaspoon vanilla.
Transfer the frosting to a pastry bag; pipe large rosettes on top of the cupcakes.