In a grill with a cover, prepare a medium-hot fire for direct-heat cooking.
For caramelized onions, combine onion, pepper sauce, broth, vinegar, oil, garlic, and brown sugar in a 10-inch nonstick skillet with a lid. When coals are ready, place covered pan on grill rack. Cook onion mixture for 15 to 20 minutes, stirring occasionally, until onions are caramelized and most of liquid is evaporated. Remove pan from grill and set aside.
For spread, combine sour cream, goat cheese, and mixed herbs, mix and set aside.
For burgers, place ground beef in a large bowl. Add onion, Zinfandel, herbs, pepper sauce, salt, pepper, and chili powder; mix gently. Shape beef mixture into 6 thin patties, adding a slice of butter in the middle to retain moisture.
Brush grill rack with vegetable oil. Place patties on grill rack, cover, and cook about 4 minutes. Turn and continue cooking until cooked to desired doneness.
Meanwhile, place saucepan with cheese spread on outer edge of grill rack to warm cheese mixture just until it reaches a very soft, spreading consistency. Remove saucepan from grill and set aside.
During final minutes of grilling patties, arrange avocado slices on a rimmed nonstick perforated grilling pan coated lightly with balsamic vinegar, lime juice, and lime zest mixture, and grill alongside patties for 1 to 2 minutes, turning as necessary. When avocados are nicely grilled remove from grill. When patties are cooked, remove from grill, stacking to keep warm. Place rolls, cut side down, on outer edges of grill to toast lightly.
Assemble burgers by placing a patty on a bun, followed by spread, then 3 avocado slices and 4 roasted red pepper slices. top with romaine lettuce and caramelized onions.
Put the bun on top and enjoy!