Combine Hellmann's® or Best Foods® Real Mayonnaise, vinegar and garlic in medium bowl. Remove 1/4 cup to small bowl; set aside. Add Gruyère cheese and milk to remaining Mayonnaise mixture; set aside.
Heat oil in large nonstick skillet over medium heat and cook onions and thyme, covered, stirring occasionally, until tender, about 5 minutes. Increase heat to medium-high and cook, uncovered, stirring occasionally, until golden brown, about 6 minutes. Stir in Mayonnaise-cheese mixture; remove from heat. Cover to keep warm and set aside.
Grill, broil or pan-fry burgers, turning once, until done, about 10 minutes for medium-rare. Spread buns with reserved Mayonnaise mixture. Top bun bottoms with burgers, then onion mixture and if desired, your favorite burger toppings.