Preheat the oven to 375 degrees F. Grab a 12-inch round pizza pan and, if desired, line it with parchment paper. Otherwise, leave the pan ungreased. Set aside.
Place a large skillet over medium heat. Cook the ground beef until browned and no longer pink, breaking up the meat as it cooks. Use a paper towel to soak up any excess grease in the skillet.
Remove the skillet from the heat and stir in the ketchup, mustard, and pickles until well combined. Set aside to cool slightly.
Place a 6-inch wide bowl upside down on the prepared pizza pan. Unroll the crescent roll dough and separate each tube into triangles. Arrange the triangles in a circle around the bowl, with the larger ends towards the center. They should overlap halfway, creating the shape of a sun. Seal the overlapping dough edges together by pressing them firmly.
Spoon the ground beef mixture in a ring over the wider end of the crescent rolls. Then cut the cheese slices in half and place them over the meat. Remove the bowl from the center.
Fold the narrow end of each triangle over the filling and carefully tuck it under the inside dough edge to secure. The filling will not be fully covered and will show between the dough pieces.*Tip: I found it easier to fold over 1 dough triangle at a time, and gently tuck it under with a fork or butterknife.
Bake for 18 minutes until golden brown. Remove from the oven. One at a time, brush each pastry section with melted butter and then sprinkle with sesame seeds. This will help the seeds stick before the butter soaks into the crust.
Place a bowl of fry sauce or your favorite dipping sauce in the center of the ring. Arrange shredded lettuce around the bowl and serve.