Center a rack in the oven and preheat the oven to 375°F. Line a jelly-roll pan with parchment paper and keep it close at hand. Cut 12 pieces of string into 6 inch lengths and butter the strings.

Stack the sheets of phyllo on a work surface. Working with one sheet of phyllo at a time and keeping the others covered with a kitchen towel, brush a sheet with butter and sprinkle it with Parmesan cheese. Cover with a second piece of phyllo and give it a coating of butter and a sprinkling of cheese. Using a long sharp knife and a ruler as a guide, cut the sheets lengthwise in half and crosswise in thirds. Place 1 scallop in the center of each of the 6 rectangles, top with a little sliced scallion, and add a dab of pesto. Gather up the corners of the rectangles, tie the purses with the buttered strings, and place them on the jellyroll pan. Repeat with the remaining phyllo and scallops.

Baking the Purses

Bake the purses for about 12 minutes, or until golden brown. Snip off the strings and serve immediately,

You can assemble the purses early in the day and keep them covered in the refrigerator until you are ready to bake them, at which point they may need an extra 2 or 3 minutes of baking time. Once baked, the purses should be served quickly.