Cut onions in half and slice thinly. Heat butter and oil together in a large skillet over medium low heat. Add the sliced onions, ½ teaspoon salt, ¼ teaspoon pepper, and thyme. Cook the onions slowly, stirring occasionally, until deeply browned and caramelized, about 45 minutes. Remove the thyme sprigs, raise heat to high, and add the balsamic vinegar. Cook, stirring, until all the vinegar has evaporated. Can be made several days ahead, store in a covered container in the refrigerator. Reheat in microwave or on stove-top before using.
Mix the mayonnaise and sriracha together until fully combined. Refrigerate until ready to serve.
Prepare the grill for direct heat. Combine the ground meats. Divide into 6 equal portions and shape into patties about ¾-inch thick. Make a deep depression in the center of the patties. Brush both sides of the patties with oil and season with salt and pepper. Grill for 4 minutes, flip the burgers and grill for another 4 – 5 minutes for medium-rare.
Cut the Kaiser rolls in half, spread the cut surfaces with melted butter and grill for 1 – 2 minutes.
To serve, spread the bottom roll with some of the mayonnaise mixture, top with lettuce, a tomato slice, burger patty, and some caramelized onions.