Preheat your grill or skillet over medium-high heat until hot and slightly shimmering, ready for the patties.
Slice the pumpkin or butternut squash into thin, even rounds, about 1/4-inch thick. Arrange them on a baking sheet lined with parchment and roast in the oven at 180°C (355°F) for 20-25 minutes, until the edges are caramelized and the flesh is tender.
While the pumpkin roasts, form the ground beef into four equal patties, about 3/4-inch thick. Season each generously with salt, pepper, and smoked paprika, pressing lightly to keep their shape.
Place the beef patties on the hot grill or skillet. Cook for about 4 minutes per side, until they develop a deep brown crust and juices run clear. Use tongs to handle them gently.
In the last minute of cooking, split the burger buns and toast the cut sides on the grill or skillet until golden brown and slightly crispy.
Once the pumpkin slices are done, remove them from the oven and let them cool slightly. They should be tender and caramelized with slightly crispy edges.
Assemble each burger by placing a cooked patty on the toasted bottom bun. Top with a roasted pumpkin slice, a slice of cheese if desired, and a handful of greens.
Add a generous dollop of spicy aioli on top of the greens for a flavorful kick. Then, cap with the top bun.
Serve the Jack O' Lantern Burgers hot, with the roasted pumpkin slices peeking out and the cheese melted over the juicy patties. Enjoy the playful, cozy flavors of fall!