Brush the sheet cake with the cold, flavored simple syrup. Use only enough so the liquid penetrates to the other side.
Spread the sheet cake with the pistachio buttercream.
Start rolling up the sheet cake by pinching a short end into a tight roll.
Roll up the sheet cake by lifting up the parchment paper on the side facing you and then by rolling with your hands, as tightly as you can. Alternate between pressing, squeezing, and rolling.
When the roll is completed, tuck under the parchment paper and push against the roll with the side of your hand, tightening it as much as possible without causing the filling to ooze out the ends.