In a large bowl, fold the onions into the ground beef, then add the Worcestershire, garlic powder, onion powder and some salt and pepper.
In a small bowl, mix together the Cheddar and Jack cheeses.
Form the meat mixture into 8 thin patties. In 4 patties, use your thumb to make a dent in the middle; fill the dent with some of the cheese. Sandwich with the remaining 4 patties, sealing the edges to close the cheese inside.
Prepare a grill for medium-high heat. Lightly oil the grill grates.
Cook the burgers to the desired doneness, 4 to 5 minutes per side. Grill the mushrooms and onions until tender and charred, about 5 minutes per side. Toast the buns, cut-side down, on the grill until marked, 1 to 2 minutes.
In a small bowl, stir together the mayonnaise and sriracha.
Place the patties on the buns and top with arugula and grilled onions and mushrooms. Finish with a drizzle of sriracha mayonnaise and the top buns.
This recipe was created by a contestant during a cooking competition. It has not been tested for home use.