Argentinians typically serve their grilled meats with Chimichurri, a bright green sauce of chopped fresh parsley, garlic and olive oil. Serve with burgers to liven up the flavor.
For the Chimichurri, place parsley, garlic, oregano, fennel seed and cayenne pepper in food processor; cover. Pulse until garlic is chopped. With food processor running, gradually add oil and lemon juice. Stir in sea salt. Transfer 1/2 cup of the Chimichurri to large bowl. Reserve remaining Chimichurri until ready to serve.
For the Burgers, add ground beef to Chimichurri in bowl. Mix until well blended. Shape into 4 patties.
Grill over medium heat 4 to 6 minutes per side or until burgers are cooked through (internal temperature of 160°F). Add cheese slices to burgers 1 minute before cooking is completed. Toast rolls on the grill, open-side down, about 30 seconds.
Serve burgers on rolls with red onion and reserved Chimichurri.