Preheat a Belgian waffle iron according to manufacturer directions.

Combine olive oil, parsley, garlic, and capers in a mini food processor or immersion blender.

Process into a semi-smooth sauce and season with salt and pepper.

Lightly dust a work surface with flour.

Lay out puff pastry sheet, lightly flour the top.

Roll into an approximate 16- by 16-inch square.

Spread garlic sauce on puff pastry, leaving a 1-inch border on all edges.

Layer mortadella on top, leaving a 1-inch border on all edges.

Roll puff pastry sheet away from you like a jelly roll.

Pinch seam to seal completely when rolled.

Pinch ends of puff pastry to seal.

Coil into a disk-shaped spiral.

Place spiral in the center of the preheated waffle iron.

Cook until puff pastry is deep golden brown on all surfaces.

Check that an instant-read thermometer inserted into the center registers 190 to 200°F, about 12 minutes.

Transfer to a cutting board.

Cut into wedges and serve immediately.