Chop the onion thinly and cook it slowly over medium heat in a skillet with a little oil until it becomes deep golden brown and sweet-smelling, about 15 minutes. Stir occasionally to prevent burning.
In a mixing bowl, combine the ground beef with pumpkin puree and spicy mustard. Gently mix until just incorporated, being careful not to overwork the meat.
Divide the beef mixture into four equal portions and shape each into a slightly larger patty than your buns, creating a small well in the center of each for the fillings.
Preheat your grill or skillet to medium-high heat until hot and shimmering, around 190°C (375°F). Place the patties on the grill and cook for about 4-5 minutes per side, until they develop a nice sear and the internal temperature reaches 70°C (160°F).
While the burgers cook, slice the cheddar cheese and prepare your toppings: crispy lettuce leaves and caramelized onions.
Once cooked, transfer the patties to a plate and let them rest for 3 minutes to retain their juices.
Top each burger with a slice of cheddar cheese, allowing it to melt slightly from the heat of the patty, about 1-2 minutes.
Spread a little spicy mustard on the bottom bun, then place the burger with cheese on top. Add caramelized onions and crisp lettuce, then cover with the top bun.
Serve the burger hot, with the bright orange pumpkin filling slightly oozing out and a golden-brown crust on the beef. Enjoy the playful, festive flavors!