Step 1

Preheat oven to 375°F and spray a 10 x 15-inch jelly roll pan with nonstick spray; line pan with parchment paper and spray parchment paper with nonstick spray.

Step 2

Whisk together flour, baking powder, baking soda, spices, and salt in a large bowl.

Step 3

Place eggs in a large mixer bowl fitted with wire whip attachment and whip on medium-high speed, gradually adding white sugar. Add brown sugar, vanilla, and molasses; whip until thick and voluminous, about 3 minutes. Add flour mixture and fold in with a rubber spatula just until combined.

Step 4

Spread the batter evenly into prepared pan and tap pan sharply to reduce air bubbles. Bake for 16 to 18 minutes, until the cake springs back to the touch. While the cake bakes, place a clean thin kitchen towel flat on the kitchen counter, and dust with 1/2 cup powdered sugar.

Step 5

Remove cake from the oven and immediately turn out onto prepared kitchen towel. Slowly and carefully peel off the parchment paper, and dust the cake with remaining 1/4 cup powdered sugar. Starting from the narrow end, carefully and gently roll up the cake with the towel. Transfer rolled up cake to a wire rack and place seam side down; let cool completely.

Step 6

For the frosting, cook 2 tablespoons butter in a heavy saucepan over medium heat, stirring constantly until it foams, turns clear, and then turns a deep brown. Pour brown butter into a mixer bowl and let cool to room temperature. Add butter and cream cheese, and beat until combined. Mix in vanilla and salt. Beat in powdered sugar on low speed until incorporated, then on medium speed until soft and creamy.

Step 7

Gently unroll the cooled cake, and use an offset spatula to spread frosting over the cake. Carefully re-roll the cake, wrap tightly in plastic wrap, and chill in the refrigerator for at least 30 minutes. Dust with powdered sugar before slicing and serving (trim any uneven edges before cutting into slices).