Preheat the oven to 350 degrees F. Butter an 11-by-17-inch rimmed baking sheet and line with parchment paper; butter the parchment and dust with flour.
Bring the cola to a simmer in a medium skillet over medium-high heat and cook until reduced to 1/2 cup, 10 to 12 minutes. Let cool. Whisk the flour, cocoa powder, baking powder, baking soda and salt in a bowl.
In a separate large bowl, whisk the granulated sugar, vegetable oil, buttermilk, eggs, food coloring, almond and vanilla extracts, and the cola syrup. Stir the dry ingredients into the wet ingredients until just combined. Spread the batter on the prepared baking sheet; bake until the cake pulls away from the pan, about 15 minutes. Let cool on the pan on a rack, 5 minutes.
Dust a kitchen towel (not terry cloth) with confectioners' sugar. Invert the cake onto the towel and peel off the parchment. Trim the cake edges. Starting with a short end, roll up the cake around the towel; let cool completely on a rack.
Make the filling: Whisk the cream cheese, 1/2 cup cream and the almond extract in a large bowl. Beat the remaining 1 cup cream and the confectioners' sugar with a mixer until soft peaks form; gradually fold into the cream cheese mixture. Chill until ready to use.
Unroll the cooled cake. Spread with the filling, then gently reroll the cake and transfer to a platter. Dust with confectioners' sugar.