Melt butter in large skillet; add onions and sprinkle with 1 teaspoon seasoning. Sauté onions until tender, about 7-10 minutes. Onions can be made ahead.
Shape ground beef into four five-inch burgers. Sprinkle 1 tablespoon seasoning over both sides of burgers. Grill burgers over direct high heat (450°-550°F) 8-10 minutes, turning once, or until internal temperature reaches 160°F. When burgers are nearly done, grill kaiser rolls cut side down, 1-2 minutes until lightly toasted.
Place burgers on bottom roll. Top each burger with equal amounts of onions and about 1 1?2 tablespoon blue cheese. Top with bun and serve with desired condiments.
Make it amazin’ with Weber® Gourmet Burger™ Seasoning.