Heat oven to 350°F/175°C convection. Line a 12-by-16-inch rimmed baking sheet with parchment.
Whisk sugar, melted butter, and oil until glossy. Add eggs and yolk and whisk until fully emulsified. Whisk in cocoa powder and red food coloring until evenly colored. Add flour, baking powder, baking soda, salt, and milk and stir just until smooth and combined.
Spread batter evenly in the prepared pan. Bake until the cake springs back lightly and a toothpick inserted shows moist crumbs, 25 to 30 minutes. Cool completely in the pan on a rack.
Cut 6 rounds with a cutter. For each cake, stack 3 layers.
In a stand mixer fitted with the whisk, beat heavy cream, cream cheese, sugar, and vanilla on medium speed until thick, smooth, and stable, 3 to 4 minutes.
Place one cake layer on a plate. Spread or pipe an even layer of cream. Repeat with remaining layers to form 3 cake layers and 3 cream layers. Finish with berries. Chill 20 minutes before serving for clean slices.