Preheat oven to 350°F and line jelly roll pan with parchment paper
Sift together flour, cocoa powder, baking powder, and salt
Beat eggs on high speed 3-4 minutes until thick and pale
Gradually add sugar and beat until fluffy
Fold in vanilla, buttermilk, vinegar, and food coloring
Gently fold in dry ingredients until just combined
Spread batter in prepared pan and bake 10-12 minutes
Dust kitchen towel with powdered sugar
Flip hot cake onto towel, remove parchment, and roll with towel inside
Cool completely rolled for 30 minutes
Beat cream cheese and butter until smooth
Add powdered sugar, vanilla bean paste, and salt, beat until fluffy
Unroll cake, spread frosting evenly, leaving 1/2 inch at edges
Roll cake back up without towel, wrap in plastic, and refrigerate 1 hour before slicing