Preheat oven to 325°F (170°C). Line a 13x9-inch rimmed baking sheet with parchment paper.

For cake: In the bowl of a stand mixer fitted with the whisk attachment, beat egg whites on high speed until doubled in size, 3 to 4 minutes. With mixer at low speed, gradually add ⅓ cup (67 grams) granulated sugar. Increase mixer speed to medium-high, and beat until thick and glossy, 1 to 2 minutes. Transfer egg white mixture to a medium bowl.

Return mixer bowl and whisk attachment to stand mixer. Add egg yolks and remaining ⅓ cup (67 grams) granulated sugar; beat at high speed until thick and pale in color, 3 to 4 minutes. Gently fold in egg white mixture just until a few white streaks remain.

In a small bowl, stir together melted butter and cream. Gently fold into batter just until combined. Sift flour onto batter; gently fold in just until no white streaks remain.

Divide batter among 6 small bowls (about 83 grams each); tint batter with food coloring as desired. Transfer each color of batter to a separate pastry bag, and cut a ½-inch opening in each tip. Pipe each color of batter into prepared pan in a row.

Bake until cake springs back when lightly pressed in center, 10 to 14 minutes. Let cool in pan on a wire rack for 10 minutes.

Lightly dust confectioners’ sugar onto cake; top with a clean kitchen towel. Place a cutting board on towel, and carefully invert cake onto towel. Gently remove pan and parchment paper. Starting at one long side, roll up cake with towel into a log. Place, seam side down, on a wire rack, and let cool completely.

For filling: In the bowl of a stand mixer fitted with the whisk attachment, beat cold cream, confectioners’ sugar, and vanilla at medium speed until medium-stiff peaks form.

Gently unroll cooled cake; spread whipped cream onto cake, leaving a ½-border on long side that is bottom seam. Gently reroll cake without towel, and place, seam side down, on a serving plate. Refrigerate until cake is chilled, about 1 hour, before serving. Best served same day. Refrigerate in an airtight container for up to 1 day.