Divide the ground beef into four equal portions and gently shape each into a round patty, keeping them slightly larger than the buns to allow for shrinkage.
Preheat your grill to medium-high heat and brush the grates lightly with oil to prevent sticking.
Place the beef patties on the grill, cooking for about 4-5 minutes per side until they develop a nice brown crust and reach your desired internal doneness.
During the last minute of cooking, top each patty with a slice of smoked cheese, allowing it to melt slightly and coat the top with a gooey layer.
While the patties cook, lightly toast the burger buns on the grill cut side down until golden and crispy, about 1-2 minutes.
Arrange the toasted buns on a platter. Place each cheesy burger patty on the bottom bun.
Decorate the burgers with playful facial features using assorted toppings—sliced olives for eyes, cherry tomatoes or jalapeños for mouths or other features, and slices of pickles or onions for additional details to create goofy monster faces.
Top each decorated burger with the bun lids and secure with toothpicks if needed to hold the features in place.
Serve immediately, with extra toppings on the side for customizing or adding more monstrous flair.