Melt butter in large skillet on medium-high heat. Add onion; cook and stir 6 to 7 minutes or until golden brown. Add mushrooms; cook and stir 2 minutes or until mushrooms are tender. Set aside.
Mix ground beef, Gravy Mix and basil in large bowl 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). Toast rolls on the grill, open-side down, about 30 seconds or until golden.
Serve burgers on toasted rolls with caramelized onions and mushrooms. Garnish with desired toppings and condiments.