Make the Onion Jam for these juicy grilled beef burgers up to two days ahead of time.
Combine the ground beef, half of the Onion Jam, the 4 ounces goat cheese, the salt, and the red pepper in a large mixing bowl. Divide mixture into 6 portions and form each portion into a patty about 1 inch thick.
Place burger patties on the lightly oiled rack of the grill directly over medium heat. Grill for 18 to 23 minutes or until an instant-read thermometer inserted in centers registers 160 degree F, turning burgers once halfway through grilling.
Grill the Texas toast, if desired. Spread 6 slices with some of the remaining Onion Jam and top each with a grilled burger patty. Top with additional goat cheese, if desired. Top with the remaining Texas toast slices. Serve with any remaining Onion Jam and, if desired, golden tomato wedges. Makes 6 burgers.
Prepare the Onion Jam for the burgers up to 2 days in advance. Cover and refrigerate until serving time.
Heat cooking oil in a large skillet over medium heat. Add yellow onions and red onions; cook and stir for 5 minutes. Stir in green onions; cook onion mixture for 25 to 30 minutes or until browned, stirring occasionally. Add balsamic vinegar and brown sugar; reduce heat. Simmer for 10 to 12 minutes or until most of the liquid evaporates. Remove from heat. Cover and chill for up to 1 week. Makes about 1-1/3 cups.