In a large bowl, mix ground elk, Worcestershire sauce, Dijon mustard, garlic powder, onion powder, salt, black pepper, and smoked paprika
Add egg and breadcrumbs if using, then gently mix until just combined
Form the mixture into 3-4 burger patties, pressing slightly in the center to prevent puffing during cooking
Heat olive oil in a skillet or grill over medium-high heat
Cook the elk burgers for about 3-4 minutes per side or until the internal temperature reaches 140-145°F for medium-rare or 160°F for well-done
Remove from heat and let rest for 5 minutes before serving
Serve on toasted buns with your favorite toppings like lettuce, tomato, cheese, and aioli