Special equipment: a 5-inch ramekin
Preheat oven to 375 degrees F. Stir together the ketchup, mayonnaise, chopped pickles and mustard in a medium bowl. Set aside.
Cook the bacon in a large skillet over medium-high heat until golden and crispy, 3 to 4 minutes per side. Drain all but 1 tablespoon of bacon drippings from the skillet. Add the onion and cook, stirring occasionally, until softened, 2 to 3 minutes. Add in the ground beef, 1/2 teaspoon salt and a few grinds of pepper and cook, breaking the meat up with a wooden spoon and scraping up any brown bits in the pan, until golden brown in spots and cooked through, 5 to 6 minutes. Transfer to a medium bowl and let cool slightly, about 15 minutes. Stir in 3/4 cup of the ketchup sauce.
Coat the back of a baking sheet with cooking spray. Unroll both cans of crescent dough and separate unto 16 triangles. Put a 5-inch ramekin in the center of the prepared baking sheet. Arrange the triangles in a ring around the ramekin so the short sides of the dough are touching the ramekin, overlapping slightly, and the pointed ends are facing outward (it should look like a giant sun).
Spoon the beef mixture over the short ends of the triangles closest to the ramekin. Cover the beef with the cheese slices. Top the cheese with the pickle slices. Remove the ramekin. Take hold of the pointed end of one of the triangles and fold it up and over the filling, tucking the tip under the bottom edge of dough to secure (the dough will not cover the filling completely but should cover the pickle slice). Repeat with the remaining triangles (there will be some gaps where you can see the beef mixture).
Bake until the dough is golden brown and the cheese is melted, about 25 minutes. Brush the ring with butter and sprinkle on the sesame seeds. Let cool for 15 minutes. Use a spatula to slide the ring off the baking sheet onto a platter. Serve with the remaining ketchup sauce.
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