Position a rack in the upper and lower thirds of the oven and preheat to 350 degrees . Lightly butter two 12-by-18-inch rimmed baking sheets, line with parchment and butter the parchment. In a small bowl, whisk together the flour, baking powder and 1/2 teaspoon salt.
Using an electric mixer with a whip attachment, beat 10 egg yolks, the vanilla and 1 cup granulated sugar at high speed until pale and fluffy, 2 to 3 minutes. Stir in the flour mixture just until incorporated. Gently fold in the melted butter and 1/4 cup orange juice.
In a clean mixer bowl with clean beaters, beat the egg whites at medium speed until frothy, 1 to 2 minutes. With the machine on, gradually sprinkle in the remaining 1 cup granulated sugar a tablespoon at a time. Once all the sugar has been added, increase the speed to high and beat until the egg whites are still moist but hold stiff peaks, 2 to 3 minutes. Fold one-quarter of the whites into the cake batter with a rubber spatula, then fold in the remaining egg whites just until no streaks remain, taking care to get the batter at the bottom of the bowl. Divide the batter between the prepared pans, smoothing evenly.
Bake the cakes, switching and rotating the pans after 10 minutes, until springy to the touch in the center and lightly golden, 16 to 18 minutes. Lay 2 non-terry kitchen towels out on the counter and dust lightly with confectioners sugar. With a serrated knife, trim around the edges of the cakes and invert onto the towels. Cover the layers with 2 other towels and let cool completely while you prepare the frosting.
Make the frosting. Using an electric mixer, beat the remaining 6 egg yolks and 2 1/4 cups confectioners sugar at medium-high speed until smooth and pale, about 2 minutes. Place the strawberries in a medium saucepan, cover and cook over medium heat, stirring occasionally, until simmering, about 3 minutes. Gradually whisk the hot strawberry puree into the yolk mixture. Transfer the mixture into the saucepan, stir in the remaining 1/2 teaspoon salt and cook, stirring, until the temperature reaches 170 degrees on an instant-read thermometer, 5 to 6 minutes. Transfer the saucepan to an ice-water bath, stirring occasionally until cold (alternatively, let cool, then cover and refrigerate overnight).
Using the electric mixer, beat the remaining 6 sticks butter at high speed until fluffy, about 5 minutes. Beat in the chilled strawberry mixture 1/2 cup at a time at low speed. Beat in the remaining 2 teaspoons orange juice until fluffy. Add 1 or 2 drops red food coloring, if using.
Assemble the cake. With a serrated knife, cut each cake layer lengthwise into 4 even strips, keeping the strips close together. Spread 1 1/2 cups of the strawberry buttercream onto each strip. Roll up 1 of the strips lengthwise into a snug spiral like a jelly roll. Place the roll on the end of another strip and roll up the second strip around the roll-this will be the center of the cake. Place the roll cut side down in the middle of a 10-inch round cake board. Pick up another frosted strip and place one of its ends at the end of the rolled strips on the board, frosting side in toward the roll; wrap it around to enlarge the cake. Continue with the remaining frosted cake strips, taking care to make the ends meet and rolling snugly.
Frost the top and sides of the cake (reserving some frosting for piping). Decorate the cake perimeter with the cigarette cookies and pipe a fluted edge of frosting on the top edge of the cake.