“Quick” puff pastry, also known as “flaky pastry” (England), “American” puff pastry, or demi-feuilleté, is a shortcut hybrid of true puff pastry and American flaky pie pastry. Again there are many versions. Usually some or all of the fat is cut coarsely into the flour as for pie pastry, cold water added to make a dough, any remaining fat sandwiched with the dough, and the dough then folded and rolled out two or three times, with periods of refrigeration to rechill the fat and relax the gluten.
Even quick puff pastry dough takes a couple of hours to make. Fortunately these doughs freeze well and are commercially available in frozen form.